CONDENSED CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY - USD ($) $ in Thousands	Total	Class A Common Stock	Common Stock Class A Common Stock	Common Stock Class B Common Stock	Additional Paid-in Capital	Retained Earnings	Non-controlling Interest	Accumulated Other Comprehensive Income (Loss)
Beginning balance (in shares) at Sep. 30, 2021			13,277,000	1,819,000
Beginning balance at Sep. 30, 2021	$ 254,833		$ 133	$ 18	$ 150,825	$ 74,952	$ 28,905	$ 0
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	23,486					20,019	3,467
Distributions to members	(619)					(442)	(177)
Non-controlling interest in subsidiary	19,311						19,311
Exchange of B shares for A shares (in shares)			389,000	(389,000)
Exchange of B shares for A shares	0		$ 4	$ (4)	7,405		(7,405)
Establishment of liabilities under tax receivable agreement and related changes to deferred tax assets associated with increases in tax basis	(283)				(283)
Shares issued upon vesting of equity-based awards, net of tax withholding (in shares)			53,000
Shares issued upon vesting of equity-based awards, net of tax withholding	(468)		$ 1		(469)
Shares issued in connection with a business combination (in shares)			133,000
Shares issued in connection with a business combination	6,834		$ 1		6,833
Equity-based compensation	2,100				2,100
Ending balance (in shares) at Dec. 31, 2021			13,852,000	1,430,000
Ending balance at Dec. 31, 2021	305,194		$ 139	$ 14	166,411	94,529	44,101	0
Beginning balance (in shares) at Sep. 30, 2021			13,277,000	1,819,000
Beginning balance at Sep. 30, 2021	254,833		$ 133	$ 18	150,825	74,952	28,905	0
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	65,840
Currency translation adjustment	0
Ending balance (in shares) at Mar. 31, 2022			13,879,000	1,430,000
Ending balance at Mar. 31, 2022	348,935		$ 139	$ 14	168,095	130,560	50,127	0
Beginning balance (in shares) at Dec. 31, 2021			13,852,000	1,430,000
Beginning balance at Dec. 31, 2021	305,194		$ 139	$ 14	166,411	94,529	44,101	0
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	42,354					36,297	6,057
Distributions to members	(871)					(266)	(605)
Exchange of B shares for A shares	0				(574)		574
Shares issued upon vesting of equity-based awards, net of tax withholding (in shares)			27,000
Shares issued upon vesting of equity-based awards, net of tax withholding	(455)				(455)
Equity-based compensation	2,713				2,713
Currency translation adjustment	0
Ending balance (in shares) at Mar. 31, 2022			13,879,000	1,430,000
Ending balance at Mar. 31, 2022	348,935		$ 139	$ 14	168,095	130,560	50,127	0
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Repurchase and Retirement of Treasury (in shares)		(73,487)
Repurchase and Retirement of Treasury		$ (1,900)
Ending balance (in shares) at Mar. 31, 2023			14,306,000	1,430,000
Ending balance at Mar. 31, 2023	486,377		$ 143	$ 14	184,520	235,754	65,936	10
Beginning balance (in shares) at Sep. 30, 2022			14,212,000	1,430,000
Beginning balance at Sep. 30, 2022	444,877		$ 142	$ 14	180,296	204,880	59,552	(7)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	11,428					8,900	2,528
Distributions to members	(319)					(10)	(309)
Shares issued upon vesting of equity-based awards, net of tax withholding (in shares)			86,000
Shares issued upon vesting of equity-based awards, net of tax withholding	(754)		$ 1		(755)
Equity-based compensation	2,572				2,572
Currency translation adjustment	11						1	10
Ending balance (in shares) at Dec. 31, 2022			14,298,000	1,430,000
Ending balance at Dec. 31, 2022	457,815		$ 143	$ 14	182,113	213,770	61,772	3
Beginning balance (in shares) at Sep. 30, 2022			14,212,000	1,430,000
Beginning balance at Sep. 30, 2022	444,877		$ 142	$ 14	180,296	204,880	59,552	(7)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	38,465
Repurchase and Retirement of Treasury (in shares)		(63,353)
Repurchase and Retirement of Treasury		$ (1,600)
Currency translation adjustment	19
Ending balance (in shares) at Mar. 31, 2023			14,306,000	1,430,000
Ending balance at Mar. 31, 2023	486,377		$ 143	$ 14	184,520	235,754	65,936	10
Beginning balance (in shares) at Dec. 31, 2022			14,298,000	1,430,000
Beginning balance at Dec. 31, 2022	457,815		$ 143	$ 14	182,113	213,770	61,772	3
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	27,037					22,804	4,233
Distributions to members	(72)					(2)	(70)
Shares issued upon vesting of equity-based awards, net of tax withholding (in shares)			27,000
Shares issued upon vesting of equity-based awards, net of tax withholding	(386)				(386)
Shares issued as part of employee stock purchase plan (in shares)			44,000
Shares issued as part of employee stock purchase plan	1,063		$ 1		1,062
Repurchase and Retirement of Treasury (in shares)			(63,000)
Repurchase and Retirement of Treasury	(1,579)		$ (1)		(760)	(818)
Equity-based compensation	2,491				2,491
Currency translation adjustment	8						1	7
Ending balance (in shares) at Mar. 31, 2023			14,306,000	1,430,000
Ending balance at Mar. 31, 2023	$ 486,377		$ 143	$ 14	$ 184,520	$ 235,754	$ 65,936	$ 10