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 G(e) and G(nu) 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 less than or similar to theta(13) less than or similar to 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.