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Non-Controlling Interest - Impact on Equity due to Changes in Ownership Interest (Details) - USD ($) $ in Thousands | 12 Months Ended
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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

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