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Equity-Based Compensation - Additional Information (Details) - USD ($) $ / shares in Units, $ in Thousands | 12 Months Ended |  |  |
--- | --- | --- | --- | ---
Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021 | May 31, 2021 | Sep. 30, 2020 | May 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Income tax benefits related to equity-based compensation | $ 785 | $ 468 | $ 1,083 |  |  |
Granted, weighted average grant date fair value (in USD per share) | $ 13.68 |  |  |  |  |
Stock options outstanding (in shares) | 8,576,670 | 8,222,322 |  |  |  |
Options exercisable at end of period (in shares) | 5,586,736 |  |  |  |  |
Unrecognized compensation expense related to unvested options at end of period | $ 23,395 |  |  |  |  |
Period for recognition of unrecognized compensation cost | 2 years 1 month 6 days |  |  |  |  |
Fair value of stock options that vested | $ 24,652 |  |  |  |  |
Restricted stock units |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Period for recognition of unrecognized compensation cost | 3 years 1 month 6 days |  |  |  |  |
Granted, weighted average exercise price (in USD per share) | $ 25.28 |  |  |  |  |
Cost not yet recognized, amount | $ 12,126 |  |  |  |  |
2018 Equity Incentive Award Plan |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Shares available for grant under the plan (in shares) | 1,075,549 |  |  |  |  | 3,500,000
Additional Class A common shares added at the beginning of calendar year as percentage of common stock outstanding at end of previous year |  |  |  |  |  | 4.00%
2020 Equity Incentive Award Plan |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Shares available for grant under the plan (in shares) | 1,154,571 |  |  | 3,000,000 | 1,500,000 |

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