Is there a way to select a group in the Groups Pane (left one in the 3-pane view) and have any subgroups within that group be displayed in the upper right-hand pane?
No, there is not. The view that approaches this is “Split” view. “Columns” view also separates parent and child groups into different panels of the view. You can also hoist a group’s children into their own window by double clicking the parent.
Putting child groups into the upper right pane of “3 Pane” view presents a logical problem. If you see the parent group in the left hand panel and its children in the upper right panel, then where would grandchild, great grandchild, etc., groups be displayed? The views quickly run out of panels in which to place descendants.