11. All 24 units have absolute value 1 and therefore lie in the unit quaternion group Sp ( 1 ). 12. The Schur multiplier of the quaternion group is trivial, but the Schur multiplier of dihedral 2-groups has order 2. 13. The dihedral groups are both very similar to and very dissimilar from the quaternion groups and the semidihedral groups. 14. The quaternion group has normal subgroups of order 4 and 2 but is not a [ semi ] direct product. 15. For instance, he shows " a Hamilton group of order 2 " a " has quaternion groups as subgroups ". 16. The quaternion group consisting of the 8 Lipschitz units forms a normal subgroup of 2 " O " of index 6. 17. More generally, when " n " is a power of 2, the dicyclic group is isomorphic to the generalized quaternion group . 18. Finally, there is the generalized quaternion group of order 16 . talk ) 15 : 20, 26 April 2015 ( UTC) 19. The quaternion group consisting of the 8 Lipschitz units forms a normal subgroup of 2 " T " of index 3. 20. The elements " x " and " y " generate a normal subgroup isomorphic to the quaternion group of order 8.
