Semidirect product of Z3 and D8 with action kernel V4

Definition
This group is defined as follow: it is the external semidirect product of cyclic group:Z3 by dihedral group:D8 where the action of the latter on the former is given by a homomorphism $$D_8 \to \operatorname{Aut}(\mathbb{Z}_3)$$ whose kernel is one of the Klein four-subgroups of dihedral group:D8. Note that the homomorphism is completely specified by its kernel because there is a unique isomorphism between any two groups isomorphic to cyclic group:Z2.