Why D2 and z12 are not isomorphic?

D2, the dihedral group of order 4, consists of rotations and reflections of a square, while Z12, the cyclic group of order 12, is generated by the addition of integers modulo 12. D2 is not cyclic, as it cannot be generated by a single element, whereas Z12 is cyclic, generated by 1. Furthermore, the structure of the groups differs: D2 has elements of order 2 (the reflections) and elements of order 4 (the rotations), while Z12 has elements of various orders that are consistent with a cyclic structure. Hence, their different algebraic structures confirm that D2 and Z12 are not isomorphic.