Earnings Per Share - Schedule of Basic and Diluted Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 24, 2023	Feb. 25, 2022	Feb. 24, 2023	Feb. 25, 2022
Earnings Per Share [Abstract]
Net income (loss) attributable to SGH – Basic and Diluted	$ (27,219)	$ 2,458	$ (22,227)	$ 22,485
Weighted-average shares outstanding – Basic (in shares)	49,116	49,522	49,039	49,267
Dilutive effect of equity plans and convertible notes (in shares)	0	8,114	0	6,868
Weighted-average shares outstanding – Diluted (in shares)	49,116	57,636	49,039	56,135
Earnings (loss) per share:
Basic (in usd per share)	$ (0.55)	$ 0.05	$ (0.45)	$ 0.46
Diluted (in usd per share)	$ (0.55)	$ 0.04	$ (0.45)	$ 0.40