11. One of the simplest examples of a nonabelian group is the dihedral group of order 6. 12. It is the dihedral group of order 2, also known as the Klein four-group. 13. For an example, the lattice of subgroups of the dihedral group of order 8 is not modular. 14. The dihedral groups are both very similar to and very dissimilar from the quaternion groups and the semidihedral groups. 15. The dihedral group Z 2 & times; Z 2, generated by pairs of order-two elements. 16. For this reason the dicyclic group is also known as the "'binary dihedral group " '. 17. If the flower also has 3 lines of mirror symmetry the group it belongs to is the dihedral group D3. 18. Hence the dihedral group " D " 5 acts faithfully on this subset of Young's lattice. 19. The dihedral group of order 8 is isomorphic to the permutation group generated by ( 1234 ) and ( 13 ). 20. This group is in fact the smallest non-abelian group, the dihedral group " D " 3:
