Help with intersect faces

DFB

I cannot, for the life of me, figure out how to intersect faces. Here is a simple example:
Intersect Faces Example.skp

This example shows four groups. I would like to intersect the faces and delete the unwanted parts - for example, the ends sticking out should be removed.

I feel stupid because this should not be difficult. I can do it if I explode each group, select all, and intersect faces. Is that the only way to do this intersection? I ask, because I have had to do it that way on complex intersections and the cleanup takes a long time.

Thanks for any advice/tips.

DFB

Sorry about the example - I did not see that my AddBlocker was preventing the attachment. Here is an attempt after disabling AddBlocker:

Intersect Faces Example.skp

TIG

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 ! ]