Homomorphisms and Isomorphisms · Superchallenge problem

The quaternion group $Q_8 = \{1,-1,i,-i,j,-j,k,-k\}$ (order $8$) satisfies $i^2=j^2=k^2=-1$ and $ij=k$, $ji=-k$ (and cyclic variants). Find $|\operatorname{Aut}(Q_8)|$.