$ K \rtimes_{\phi_1} C \cong K \rtimes_{\phi_2} C$ when $\phi_1(C), \phi_2(C)$ are conjugated and $C$ is a product of two cyclic groups

Question

I know the following result:

Let $C$ be a finite cyclic group, $K$ a finite group such that there exist homomorphisms $\phi_1,\phi_2$ $\phi_i:C \to Aut(K) $ such that $\phi_1(C), \phi_2(C)$ are conjugated subgroups of $Aut(K)$. Then the semidirect products $ K \rtimes_{\phi_1} C \cong K \rtimes_{\phi_2} C$.

I want to know if this result it's true if $C$ is a product of two cyclic groups. I need this result for at least the case of two products of cyclic groups. In the worst scenario, I want to know if it's true when $C$ is the Klein-Group.