It is not a good idea to show large groups on the showgroups page.
About the error - that is a server issue. You need to contact your hosting provider and request them to increase the value for your mysql setting max_allowed_packet in the my.cnf file and then restart MySQL. I would try 32M and if that doesnt work, then try 64M.
You can see more about the error in the manual here -
https://www.vbulletin.com/docs/html/...t_mysql_errors