  In this note, we give a way to classify $\mathbb Q$-Fano compactifications of
a semisimple group $G$. We will prove that there are only finitely many such
$\mathbb Q$-Fano $G$-compactifications, which admits (singular)
K\"ahler-Einstein metrics. As an application, this improves a former result in
arXiv:2001.11320.
