Under Linux, setgid is implemented like the POSIX version with the _POSIX_SAVED_IDS feature. This allows a setgid (other than root) program to drop all of its group privileges, do some un-privileged work, and then re-engage the original effective group ID in a secure manner.
If the user is root or the program is setgid root, special care must be taken. The setgid function checks the effective gid of the caller and if it is the superuser, all process related group ID's are set to gid. After this has occurred, it is impossible for the program to regain root privileges.
Thus, a setgid-root program wishing to temporarily drop root privileges, assume the identity of a non-root group, and then regain root privileges afterwards cannot use setgid. You can accomplish this with the (non-POSIX, BSD) call setegid.