Coxeter groups and the PMNS matrix

We discuss the symmetries of the Lagrangian of the leptonic sector. We consider the case when this symmetry group is a Coxeter group. The number of elements of the PMNS matrix predicted by this group structure would depend on the number of generators of this group. We analyze finite Coxeter groups with 2 to 4 generators and even finite subgroups of infinite Coxeter groups with 4 generators and show which of them can give results that are consistent with experimental data.