A trionic subgroup is an index 3 subgroup. Johnson defines a trionic subgroup with operator ⅄, index 3. For rank 2 Coxeter groups, [3], the trionic subgroup, [3 ] is [ ], a single mirror. And for [3 p ], the trionic subgroup is [3 p ] ≅ [ p ]. Given , with generators {0,1}, has 3 trionic subgroups. They can be differentiated by putting the ⅄ symbol next to the mirror generator to be removed, or on a branch for both: [3 p,1 ] = = , = , and [3 p ] = = with generators {0,10101}, {01010,1}, or {101,010}.