[18, 12, [2, 2, 2, 2, 2, 2, 2, 2, 6], "possibly_metacyclic, not_abelian"]
[18, 12, [2, 2, 2, 2, 2, 2, 2, 3, 3], ""]
[18, 10, [2, 2, 2, 2, 2, 2, 5, 5, 5], "possibly_cyclic, possibly_metacyclic"]
[18, 8, [2, 2, 4, 4, 4, 4, 4, 4, 4], "possibly_metacyclic"]