CONDENSED CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY - USD ($) shares in Thousands, $ in Thousands	Common Stock [Member] Class A Common Stock [Member]	Common Stock [Member] Class B Common Stock [Member]	Additional Paid-in Capital [Member]	Retained Earnings [Member]	Non-controlling Interest [Member]	Accumulated Other Comprehensive Income (Loss) [Member]	Total
Beginning balance at Sep. 30, 2021	$ 133	$ 18	$ 150,825	$ 74,952	$ 28,905	$ 0	$ 254,833
Beginning balance (in shares) at Sep. 30, 2021	13,277	1,819
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	$ 0	$ 0	0	20,019	3,467	0	23,486
Distributions to members	0	0	0	(442)	(177)	0	(619)
Non-controlling interest in subsidiary	0	0	0	0	19,311	0	19,311
Exchange of B shares for A shares	$ 4	$ (4)	7,405	0	(7,405)	0	0
Exchange of B shares for A shares (in shares)	389	(389)
Establishment of liabilities under tax receivable agreement and related changes to deferred tax assets associated with increases in tax basis	$ 0	$ 0	(283)	0	0	0	(283)
Shares issued upon vesting of equity-based awards, net of tax withholding	$ 1	$ 0	(469)	0	0	0	(468)
Shares issued upon vesting of equity-based awards, net of tax withholding (in shares)	53	0
Shares issued in connection with a business combination	$ 1	$ 0	6,833	0	0	0	6,834
Shares issued in connection with a business combination (in shares)	133	0
Equity-based compensation	$ 0	$ 0	2,100	0	0	0	2,100
Currency translation adjustments							0
Ending balance at Dec. 31, 2021	$ 139	$ 14	166,411	94,529	44,101	0	305,194
Ending balance (in shares) at Dec. 31, 2021	13,852	1,430
Beginning balance at Sep. 30, 2022	$ 142	$ 14	180,296	204,880	59,552	(7)	444,877
Beginning balance (in shares) at Sep. 30, 2022	14,212	1,430
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	$ 0	$ 0	0	8,900	2,528	0	11,428
Distributions to members	0	0	0	(10)	(309)	0	(319)
Shares issued upon vesting of equity-based awards, net of tax withholding	$ 1	$ 0	(755)	0	0	0	(754)
Shares issued upon vesting of equity-based awards, net of tax withholding (in shares)	86	0
Equity-based compensation	$ 0	$ 0	2,572	0	0	0	2,572
Currency translation adjustments	0	0	0	0	1	10	11
Ending balance at Dec. 31, 2022	$ 143	$ 14	$ 182,113	$ 213,770	$ 61,772	$ 3	$ 457,815
Ending balance (in shares) at Dec. 31, 2022	14,298	1,430