rearrange group order

It's not the only way, but I find the easiest way is to use the XML editor (Edit > XML Editor... or Shift+Ctrl+X). With that you can use the up and down arrows or drag and drop nodes, including groups, to change their order.

No need to resort to the XML Editor - you can move the current (selected) layer

a) using the commands in the 'Layer' menu:
- Raise Layer
- Lower Layer
- Layer to Top
- Layer to Bottom
<http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Layers.html#Layers-Menu>

b) using the corresponding keyboard shortcuts:
- 'Shift+Ctrl+PgUp' raise layer
- 'Shift+Ctrl+PgDn' lower layer
- 'Shift+Ctrl+Home' raise layer to top
- 'Shift+Ctrl+End' lower layer to bottom
<http://inkscape.org/doc/keys048.html#id2352063>

c) using the buttons in the 'Layers' dialog
<http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Layers.html#Layers-Dialog>

Sorry, I misread the question, ignore my previous comment. To change the stack order of groups and objects, you can use Inkscape's GUI commands:

a) the buttons on the select tool controls bar to change z-order
<http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Z-Order.html#Z-Order>

b) or the corresponding keyboard shortcuts
Home raise selection to top
End lower selection to bottom
PgUp raise selection one step
PgDn lower selection one step
<http://inkscape.org/doc/keys048.html#id2352506>

To select next object(s)/group(s) below the currently selected object under the pointer, use 'Alt+click' to 'Select Under':
<http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Select.html#Select-Mouse>