Finding the normal subgroups in a semidirect product

Question

Let the group $A=\cdots\times\mathbb{Z}_{-1}\times\mathbb{Z}_{0}\times\mathbb{Z}_{1}\times\cdots$ with $\mathbb{Z}_{i}=\left\langle a_{i}\right\rangle $ and $\alpha:a_{i}\rightarrow a_{i+1}$ an automorphism of $A$. Consider the group $G=\left\langle \alpha\right\rangle \rtimes A$ (semidirect product). How can I find the normal subgroups of $G$ contained in $A$?

Thanks!