Groups of order 8

Up to isomorphism there are five groups of order \(8\). The abelian ones are \[ \ZZ/8\ZZ,\qquad\ZZ/4\ZZ\times\ZZ/2\ZZ,\qquad(\ZZ/2\ZZ)^3, \] and the nonabelian ones are the dihedral group \(D_4\) of order \(8\) and the quaternion group \(Q_8\).