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 27, 2022	May 28, 2021	May 27, 2022	May 28, 2021
Earnings Per Share [Abstract]
Net income (loss) attributable to SGH – Basic and Diluted	$ 24,113	$ (7,211)	$ 46,598	$ 660
Weighted-average shares outstanding – Basic (in shares)	50,095	48,071	49,543	48,542
Dilutive effect of equity plans and convertible notes (in shares)	4,903	0	6,213	2,625
Weighted-average shares outstanding – Diluted (in shares)	54,998	48,071	55,756	51,167
Earnings (loss) per share:
Basic (in usd per share)	$ 0.48	$ (0.15)	$ 0.94	$ 0.01
Diluted (in usd per share)	$ 0.44	$ (0.15)	$ 0.84	$ 0.01