It is possible to create a subgroup, using profile sets. This allows you to simply add members to a profile set and the create the subgroup from that, rather than having to create a group and then add members or assign a profile set to it. For example, if you want to make a governors page on the cLc, you could add all of the governors to the governors profile set, and then make the governors profile set a subgroup.
To create a subgroup from a Profile set: