Sorry, I mis-typed 'postqueue'.
Try this instead.
Here is what happens on my system.
As root:
# chmod g-s /usr/sbin/postqueue
# ls -l /usr/sbin/postqueue
-rwxr-xr-x 1 root postdrop 60072 Dec 23 18:08 /usr/sbin/postqueue
# chmod 777 /var/spool/postfix/public
# ls -ld /var/spool/postfix/public /var/spool/postfix/public/showq
drwxrwxrwx. 2 postfix postdrop 4096 Jan 2 18:30 /var/spool/postfix/public
srw-rw-rw- 1 postfix postfix 0 Jan 2 18:30 /var/spool/postfix/public/showq
# su wietse
As non-root:
wzv$ strace -e connect postqueue -p |& grep showq
connect(4, {sa_family=AF_UNIX, sun_path="public/showq"}, 110) = 0
wzv$ exit
Back as root:
# chmod 710 /var/spool/postfix/public
# ls -ld /var/spool/postfix/public
drwx--x---. 2 postfix postdrop 4096 Jan 2 18:30 /var/spool/postfix/public
# chmod g+s /usr/sbin/postqueue
# ls -l /usr/sbin/postqueue
-rwxr-sr-x 1 root postdrop 60072 Dec 23 18:08 /usr/sbin/postqueue
Wietse