On semi-direct product of groups

There is a generalization in this paper of the theorem for Cm ⋊ C4 with m ∈ Z in some special cases to explain the structure of groups that are isomorphic to Cm ⋊ C4 and to compute the number of subgroups of the group Cpa ⋊ C4 where p is an odd prime and 1 ≤ α ≤ 2. It is probable that the number of subgroups is σ(pα) + 6.