Many of the crystallographic point groups share the same internal structure. For example, the point groups , 2, and m contain different geometric symmetry operations, (inversion, rotation, and reflection, respectively) but all share the structure of the cyclic group C. All isomorphic groups are of the same order, but not all groups of the same order are isomorphic. The point groups which are isomorphic are shown in the following table:
This table makes use of cyclic groups (C, C, C, C, C), dihedral groups (D, D, D, D), one of the alternating groups (A), and one of the symmetric groups (S). Here the symbol " × " indicates a direct product.