$\DeclareMathOperator\SU{SU}\DeclareMathOperator\SL{SL}$What are the maximal closed subgroups of $ \SU_3 $?

This question is inspired by Lie subgroups of SU(3). Interesting partial answers to that question, treating only the case of connected subgroups, are given by José Figueroa-O'Farrill and Neil Strickland.

Easier example: The three maximal closed subgroups of $ \SU_2 $ are the binary octahedral group, the binary icosahedral group and the normalizer of the maximal torus. Details given here: What are the finite subgroups of $SU_2(C)$?

My attempt: The maximal closed subgroups of $ \SU_3 $ are $$ U_2\cong S(U_2\times U_1) $$ and $$ \operatorname{SO}_3(\mathbb{R}) \times C_3 \cong \langle\operatorname{SO}_3(\mathbb{R}),\zeta_3 I\rangle $$ (I think this is the full normalizer, maybe there is some extra finite order stuff? Weirdly this type of subgroup doesn't seem to show up in table 5 of Antoneli, Forger, and Gaviria - Maximal Subgroups of Compact Lie Groups) and the normalizer of the maximal torus $$ N(T)=T^2 \rtimes S_3 $$ where here the symmetric group $ S_3=W $ is the Weyl group of $ \SU_3 $. The finite maximal closed subgroups are $$ 3 \times \Sigma_{168} \;, \; 3.\Sigma_{216},\;, \; 3.\Sigma_{360} $$ where $ \Sigma_{168} \cong \SL_3(2) $ is a the simple group of order $ 168 $, $ \Sigma_{360} \cong A_6 $ is the simple group of order $ 360 $ and $ \Sigma_{216} \cong \mathbb{F}_3^2 \rtimes \SL_2(3) $ is an affine transformation group, sometimes called the Hessian group. I believe that $ 3.\Sigma_{216} $ is the full automorphism group of an extra special $ 3 $-group of order $ 27 $ of $ + $ type, $ \operatorname{Aut}(3^{2+1}_+) $.