Is there a convenient list of the maximal abelian subgroups of the projective semilinear group $\mathrm{P\Gamma L}_3(K) \cong \mathrm{PGL}_3(K) \rtimes \mathrm{Gal}(K)$ for $K$ a finite field?

This is related to this previous question about maximal abelian subgroups of $\mathrm{GL}_n$: https://mathoverflow.net/questions/200269/maximal-abelian-subgroup-of-general-linear-groups. My question is easier in that $n = 3$, but harder in that I am mod $K^\times$ and $\rtimes \mathrm{Gal}$, which is irritating enough that it would be good to have a reference if there is one.