21. There are also isomorphic copies of the binary dihedral groups of orders 8 and 12 in 2 " O ". 22. You may also want to read the article Dihedral group . talk ) 07 : 27, 19 July 2013 ( UTC) 23. I also want to classify all finite subgroups of isometries in \ mathbb { R } ^ 2 into cyclic and dihedral groups . 24. The dihedral group of order 8 ( D 4 ) is the smallest example of a group that is not a T-group. 25. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry.26. There is a superficial resemblance between the dicyclic groups and dihedral groups ; both are a sort of " mirroring " of an underlying cyclic group. 27. For " p " = 2, both the semi-direct products mentioned above are isomorphic to the dihedral group Dih 4 of order 8. 28. The Q 8 group has the same order as the dihedral group D 4, but a different structure, as shown by their Cayley and cycle graphs: 29. Both these two groups and the dihedral group are semidirect products of a cyclic group of order 2 n " 1 with a cyclic group of order 2. 30. For example, the dihedral group appears on page 419 . The coquaternion structure has also been mentioned briefly in the " Annals of Mathematics ".
