The vertices of the coclass graph G(3,2)
represent all finite 3-groups G of coclass cc(G)=2.
G(3,2) consists of finitely many sporadic groups and 16 coclass trees,
each with a single infinite main line and a structural periodicity.
The descendants of G form one of these trees, T(G).
All capable vertices represent metabelian groups (circles).
However, several terminal vertices represent non-metabelian groups (small squares).
or metabelian groups with cyclic center of order 9 (big squares).
With the aid of colors we shall characterize the punctured transfer types (not yet shown).
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