As I understand it, I should be able to group groups of objects into a hierarchy, select an object within one of the leaf groups and move the group of groups in unison.  But it seems that I can only move sibling objects together in the same leaf node group; the rest of the groups of objects in the supergroup stay put.  Is that right or is there another trick I haven't learned yet?  Thanks.

You should be able to move any group. But you need to select the "group" and drag it not the object.

Richard