Shifts Group Specific Time Clock

I have one Team for a program that includes multiple smaller groups. Members of the Team may be assigned shifts in more than one of the smaller groups, and managers can view all the smaller groups side-by-side with this setup. I turned on the Time Clock ability, but when I clock in, it only lists the Team, not the individual groups. For accounting purposes, I need to be able to track which group they worked for, but I don't see a way to do that. Am I missing something?