Classify the group (Z4 x Z2)/({0} x Z2).

I know the order of (Z4 x Z2)/({0} x Z2) is 4, and groups with order 4 are either the Klein-4 Group or Z4. I know Z4 is abelian and cyclic and the Klein-4 Group is abelian and noncyclic. I also have a theorem that states since 4 and 2 are not relatively prime, Z4 x Z2 is not cyclic. So would the group be the Klein-4 group then?