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Derivative Instruments and Hedging Activities - (Details)
3 Months Ended 6 Months Ended
Mar. 31, 2022
USD ($)
instrument
Mar. 31, 2021
USD ($)
Mar. 31, 2022
USD ($)
instrument
Mar. 31, 2021
USD ($)
Jul. 31, 2017
USD ($)
derivative
Derivative Instruments          
Number of derivative instruments held | instrument 0   0    
Interest expense $ 19,896,000 $ 23,883,000 $ 40,137,000 $ 49,861,000  
Foreign Currency Forwards          
Derivative Instruments          
Derivative instruments, expiration date     Sep. 30, 2022    
Notional Amount 27,368,000   $ 27,368,000    
Foreign Currency Forwards | Reclassification out of Accumulated Other Comprehensive Income          
Derivative Instruments          
Foreign currency forwards designated as cash flow hedges to be reclassified gain (loss)     (400,000) 400,000  
Foreign currency forwards designated as cash flow hedges to be reclassified losses into cost of goods sold over next 12 months 100,000   $ 100,000    
Interest rate caps | Variable-rate tranche | Sally Holdings, LLC          
Derivative Instruments          
Derivative instruments, expiration date     Jun. 30, 2023    
Notional Amount         $ 550,000,000
Number of interest rate caps | derivative         2
Interest expense     $ 400,000 $ 200,000  
Interest rate caps | Term loan B variable tranche | Sally Holdings, LLC          
Derivative Instruments          
Interest rate caps designated as cash flow hedges to be reclassified into interest expense over next 12 months $ 1,900,000   $ 1,900,000