Revenue from Contracts with Customers - Sources of Noninterest Income (Details) - USD ($) $ in Thousands	3 Months Ended	6 Months Ended
Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2021	Mar. 31, 2020
Revenue from contracts with customers	$ 1,238	$ 1,079	$ 2,423	$ 2,144
Gain on sale of securities		7		7
Gain on sale of SBA loans	3,239	1,229	4,506	1,990
Mortgage banking income	32,398	8,411	74,698	24,334
Increase in cash value of life insurance	174	194	360	356
Real estate lease income	149	152	296	303
Loan servicing and other income	1,775	61	2,873	231
Other noninterest income	37,735	10,054	82,733	27,221
Total noninterest income	38,973	11,133	85,156	29,365
Service charges on deposit accounts
Revenue from contracts with customers	328	441	724	950
ATM and interchange fees
Revenue from contracts with customers	513	524	1,145	1,027
Investment advisory income
Revenue from contracts with customers	365	83	499	110
Other
Revenue from contracts with customers	$ 32	$ 31	$ 55	$ 57

It represents the amount of gain (loss) on sale of securities.

No definition available.

Name:	fsfg_GainLossOnSaleOfSecurities
Namespace Prefix:	fsfg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of loan servicing and other income.

+ References

No definition available.

+ Details

Name:	fsfg_LoanServicingAndOtherIncome
Namespace Prefix:	fsfg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount represents the value of real estate lease income.

+ References

No definition available.

+ Details

Name:	fsfg_RealEstateLeaseIncome
Namespace Prefix:	fsfg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of gain (loss) from sale and disposal of integrated set of activities and assets capable of being conducted and managed for purpose of providing return in form of dividend, lower cost, or other economic benefit to investor, owner, member and participant.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3602-108585

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 810
-SubTopic 10
-Section 50
-Paragraph 1B
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=109239629&loc=SL4582445-111684

+ Details

Name:	us-gaap_GainLossOnSaleOfBusiness
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Net gain (loss) resulting from the sales of securitized, pay-through debt securities collateralized by real estate mortgage loans (mortgages).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 220
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04.13(h))
-URI http://asc.fasb.org/extlink&oid=120399700&loc=SL114874048-224260

+ Details

Name:	us-gaap_GainLossOnSalesOfMortgageBackedSecuritiesMBS
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The increase (decrease) in life insurance liability balances during the period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3602-108585

+ Details

Name:	us-gaap_IncreaseDecreaseInLifeInsuranceLiabilities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The total amount of noninterest income which may be derived from: (1) fees and commissions; (2) premiums earned; (3) insurance policy charges; (4) the sale or disposal of assets; and (5) other sources not otherwise specified.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 220
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04.13)
-URI http://asc.fasb.org/extlink&oid=120399700&loc=SL114874048-224260

+ Details

Name:	us-gaap_NoninterestIncome
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Represents the total of noninterest income derived from certain activities and assets including (for example): (1) venture capital investments; (2) bank owned life insurance; (3) foreign currency transactions; and (4) mortgage servicing rights.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 220
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04.13)
-URI http://asc.fasb.org/extlink&oid=120399700&loc=SL114874048-224260

+ Details

Name:	us-gaap_NoninterestIncomeOther
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount, excluding tax collected from customer, of revenue from satisfaction of performance obligation by transferring promised good or service to customer. Tax collected from customer is tax assessed by governmental authority that is both imposed on and concurrent with specific revenue-producing transaction, including, but not limited to, sales, use, value added and excise.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 30
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e8906-108599

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 40
-URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e9031-108599

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 41
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e9038-108599

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 32
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e8933-108599

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 32
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e8933-108599

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 4
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130543-203045

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 22
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e8736-108599

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 22
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e8736-108599

Reference 9: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 42
-URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e9054-108599

Reference 10: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130545-203045

Reference 11: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 924
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 11.L)
-URI http://asc.fasb.org/extlink&oid=6472922&loc=d3e499488-122856

+ Details

Name:	us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Details

Name:	srt_ProductOrServiceAxis=fsfg_ServiceChargesOnDepositAccountsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ProductOrServiceAxis=fsfg_ATMAndInterchangeFeesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ProductOrServiceAxis=fsfg_InvestmentAdvisoryIncomeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ProductOrServiceAxis=fsfg_OtherMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: