Semi-direct product of different groups make a same group? We can prove that both of:

$S_3=\mathbb Z_3\rtimes\mathbb Z_2$ and $\mathbb Z_6=\mathbb Z_3\rtimes\mathbb Z_2$

So two different groups (and not isomorphic in examples above) can be described as semi-direct products of a pair of groups ($\mathbb Z_3$ and $\mathbb Z_2$). I hope my question does make sense:

Is there any group which can be described as semi-direct products of two different pair of groups?

Thanks.

Such a group of smallest order is $D_8$, the Dihedral group of order 8.
Write $D_8=\langle x,y\colon x^4=y^2=1, y^{-1}xy=x^{-1}\rangle=\{1,x,x^2,x^3, y,xy,x^2y,x^3y \}$.


*

*$H=\langle x\rangle$,$K=\langle y\rangle$, then $D_8=H\rtimes K\cong C_4\rtimes C_2$.

*$H=\langle x^2,y\rangle$, $K=\langle xy\rangle$, then $D_8=H\rtimes K\cong (C_2\times C_2)\rtimes C_2$.
