G = 81gp4xC3 is Direct product 81gp4 x C_3
G has 3 minimal generators, rank 3 and exponent 9. The centre has rank 3.
The 13 maximal subgroups are: Ab(9,3,3) (4x), 81gp4 (9x).
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 3.
At present no information on the cohomology ring.