Earnings Per Share - Schedule of Basic and Diluted Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		9 Months Ended
	May 26, 2023	May 27, 2022	May 26, 2023	May 27, 2022
Earnings Per Share [Abstract]
Net income (loss) attributable to SGH – Basic and Diluted	$ (24,455)	$ 24,113	$ (46,682)	$ 46,598
Weighted-average shares outstanding – Basic (in shares)	49,380	50,095	49,152	49,543
Dilutive effect of equity plans and convertible notes (in shares)	0	4,903	0	6,213
Weighted-average shares outstanding – Diluted (in shares)	49,380	54,998	49,152	55,756
Earnings (loss) per share:
Basic (in usd per share)	$ (0.50)	$ 0.48	$ (0.95)	$ 0.94
Diluted (in usd per share)	$ (0.50)	$ 0.44	$ (0.95)	$ 0.84