  Let $G$ be a connected, complex reductive group. In this paper, we classify
$G\times G$-equivariant normal $\mathbb R$-test configurations of a polarized
$G$-compactification. Then for $\mathbb Q$-Fano $G$-compactifications, we
express the H-invariant of its equivariant normal $\mathbb R$-test
configurations in terms of the combinatory data. Based on \cite{Han-Li}, we
compute the semistable limit of a K-unstable Fano $G$-compactification. As an
application, we show that for the two K-unstable Fano $SO_4(\mathbb
C)$-compactifications, the corresponding semistable limits are indeed the limit
spaces of the normalized K\"ahler-Ricci flow.
