Homomorphisms and Isomorphisms · Challenge problem

The quaternion group $Q_8 = \{1,-1,i,-i,j,-j,k,-k\}$ (order $8$) satisfies $i^2=j^2=k^2=-1$, $ij=k$, and $ji=-k$ (with cyclic variants). How many homomorphisms are there from $Q_8$ to $S_3$ (the symmetries of $3$ labeled objects)?