How to quickly and cleanly model this without messing up topology?

Question

Please refer to the following images. This is what I have now

This is what I need to turn it into

So I need to create gaps on the rim. I tried extruding it in, deleting the extra faces and re-creating faces between the vertices, but it was very slow and the inside could not be cleanly closed for missing 1 vertex. Previously I used the boolean modifier but it seems to destroy the topology and make it harder to edit after the boolean. Another way I can think of is to loop cut it, delete some faces then re-create some faces, but it seems as slow as the first method.

Is there a good, reliable way of doing this and similar things?

Answer 1

Delete these six faces.

Select these two edges and make a face.

Do the same with the two edges next to them.

Do the same with these two.

Do the same with the pair across from them.

Done.