Determine all semidirect product of $(\mathbb{Z}_4,+)$ by $C_2 = \langle a \rangle$

Question

Determine all semidirect product of $(\mathbb{Z}_4,+)$ by $C_2 = \langle a \rangle$.

My proof: We have $\text{Aut}(\mathbb{Z}_4,+) = \{ \sigma_1,\sigma_3\}$. Define $\theta \colon C_2 \rightarrow \text{Aut}(\mathbb{Z}_4,+)$. There are two group isomorphisms, so there are two semidirect product.