This groupg even has a subgroup that is normal. The group contains three reflections and one rotation of order three. Dihedral Groups Dihedral groups are subgroups of permutation groups. Dihedral groups are all realizable in the plane. You have probably seen a dihedral group and didn't realize it.
Some flowers have petals that make dihedral groups.
Some examples are shown below. This is a D1 group. All dihedral groups contain a reflection. This is a D3 group. It contains three reflections and a rotation of order 3.