External groups require a bit more management attention than normal groups because people cannot join without an invitation. It makes sense to identify a community member with a stake in the group to manage it. Often this person is managing the efforts of the external contributor (EC) anyway.
You can easily make any community member an External Contributor Admin. Go to Admin > User Management > All Users > Active. Find the member in the list and click on the Edit link. Check the External Contributor Admin box and save.