Presentation of Interim Information (Additional Information) (Detail) $ in Millions	3 Months Ended
Dec. 31, 2018 USD ($)
Schedule of Equity Method Investments [Line Items]
Cumulative Allocated Net Income	$ 1.7
Business Capital LLC [Member]
Schedule of Equity Method Investments [Line Items]
Noncontrolling Interest, Ownership Percentage by Noncontrolling Owners	49.00%
subsidiary [Member]
Schedule of Equity Method Investments [Line Items]
Equity Method Investment, Ownership Percentage	51.00%

It represents the cumulative net income allocated during the reporting period.

No definition available.

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

- Definition

The percentage of ownership of common stock or equity participation in the investee accounted for under the equity method of accounting.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 323
-SubTopic 10
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-URI http://asc.fasb.org/extlink&oid=114001798&loc=d3e33918-111571

+ Details

Name:	us-gaap_EquityMethodInvestmentOwnershipPercentage
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The equity interest of noncontrolling shareholders, partners or other equity holders in consolidated entity.

+ References

No definition available.

+ Details

Name:	us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_ScheduleOfEquityMethodInvestmentsLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	srt_OwnershipAxis=fsfg_BusinessCapitalLLCMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=fsfg_SubsidiaryMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: