What Qt widget(s) to use for read-only, scrollable, collapsible, icon list

I'm relatively new to Qt, and am not entirely familiar with the out-of-the-box widgets. I have a somewhat (but not very) complex widget to create, and don't want to reinvent any wheels. What is the best QWidget to use as a starting point to subclass and/or QWidgets to use to compose my widget. Here is the end-result I am looking for (apologies for the crude drawing):

Key points:

• All icons will take up the same size, say 128 x 128. Ignoring the category groupings, they should all align in a nice grid.
• The widget should expand to fill all the horizontal and vertical area it can take. Expanding / shrinking horizontally may increase / decrease the number of icons shown in each row.
• Icons are grouped, and those groups should be collapsible.
• If the height of the widget exceeds its space, a vertical scrollbar should appear.