What is the size of $\text {Aut}\ (\Gamma)\ $?

Question

Consider the graph $\Gamma$

What is the size of $\text {Aut}\ (\Gamma)\ $?

I think the size of $\text {Aut}\ (\Gamma)$ is $8$ since $1$ can go to either $1$ or $4$, $2$ can go to either $2$ or $6$ and $3$ can go to either $3$ or $5.$ Am I right?

Thanks in advance.