To create a group within your class/group select Create Subgroup. Subgroups allow for further categorizing within a particular class/group, making targeted assigning possible. Unlike class/groups, the members of subgroups are unaware that they belong to it.
You can enter a name in the pop-up window and press save. The subgroup will immediately appear underneath the class name in the expanded view, and has the same action functions as the main class/group. You can add more members with the purple button, manage users with the blue button and see results with green. You cannot archive a subgroup, however you can remove all users and rename the subgroup if you no longer need it.
Having different subgroups within the same class allows you to assign different work to each subgroup, without them being aware about this differentiation.