Because of the Thanksgiving holiday in the U.S., TI E2E™ design support forum responses may be delayed from November 25 through December 2. Thank you for your patience.
From the datasheets:
SN74HC00
50 mA
CD74HC00
50 mA
SN74HC374
70 mA
CD74HC374
50 mA
SN74AC00
200 mA
CD74AC00
100 mA
SN74AC374
200 mA
CD74AC374
200 mA
74AC16374
400 mA
It's not very consistent.