  Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg
group. In these notes we classify all these groups, we find the dimension of
the spaces of $G$-invariant polynomials and we give equations for the
generators whenever the space has dimension two. Then we complete the study of
the corresponding $G$-invariant pencils of surfaces in $\mathbb{P}_3$ which we
started in math. AG/0106080. It turns out that we have five more pencils, two
of them containing surfaces with nodes.
