The coset and double-coset decompositions of the 420 subgroups of m(z)(3) o
ver bar (xyz)m(xy)1' (O(h)1') and the 236 subgroups of 6(z)/m(z)m(x)m(1)1'
(D(6h)1') with respect to each of their subgroups are calculated along with
additional mathematical properties of these groups.