  We survey the mixing patterns which can be derived from the discrete groups
Sigma (36 x 3), Sigma (72 x 3), Sigma (216 x 3) and Sigma (360 x 3), if these
are broken to abelian subgroups Ge and Gnu in the charged lepton and neutrino
sector, respectively. Since only Sigma (360 x 3) possesses Klein subgroups,
only this group allows neutrinos to be Majorana particles. We find a few
patterns that can agree well with the experimental data on lepton mixing in
scenarios with small corrections and that predict the reactor mixing angle
theta_{13} to be 0.1 <= theta_{13} <= 0.2. All these patterns lead to a trivial
Dirac phase. Patterns which instead reveal CP violation tend to accommodate the
data not well. We also comment on the outer automorphisms of the discussed
groups, since they can be useful for relating inequivalent representations of
these groups.
