Let G and K be two groups and $\phi_1$ and $\phi_2: G \rightarrow Aut(K)$ be homomorphism.
Q1: If $\phi_1$ not trivial homomorphism, can When can semidirect product of G and K using $\phi_1$ isomorphic to direct product of G and K?
Q2: Will semidirect product of G and K using $\phi_1$ and $\phi_2$ be non- isomorphic?
Q3: What will be answer to Q1 and Q2 if both groups G and K are finite cyclic groups or cyclic groups?
Q4: If answer to Q2 is no, when can semidirect product of G and K using $\phi_1$ and $\phi_2$ can be isomorphic?
And let me mention these are not homework problems.