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Non-Controlling Interest - Impact on Equity due to Changes in Ownership Interest (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Noncontrolling Interest [Abstract]      
Net loss attributable to non-controlling interest $ (1,841) $ (6,115) $ (3,382)
Redemption of common units in i3 Verticals, LLC (224) (918) (11,714)
Establishment of liabilities under a tax receivable agreement and related changes to deferred tax assets associated with increases in tax basis 4,305 11,511 15,337
Net transfers to non-controlling interests 4,081 10,593 3,623
Change from net income attributable to non-controlling interests and transfers to non-controlling interests $ 2,240 $ 4,478 $ 241