You haven't explained why you want to Intersect these faces inside the groups...
However, to get intersection lines added into faces which are INSIDE a group, you first need to edit the group [double-click it or select+context-menu > edit], then select-all [Ctrl+A] > context-menu > Intersect with Model.
New edges will be added into the edit-context where selected faces intersect other objects.
Back-out of the edit,and repeat editing and intersecting faces in other groups.
If your aim is to delete parts of a group's geometry to form 'miters' etc, then you might also want to add faces to those 'cut-ends' - by over-drawing edges.
To see what you are doing more easily you can also chose the toggle in View > Component Edit > Hide Rest of Model [ it works on Groups too ! ]
