Let $G$ be a connected semi-simple group over the ring of integers $O_F$ of a non-archimedean local field $F$. Let $\varpi_F$ be a prime element of $O_F$.
Usually parahoric subgroups of $G$ are defined as stabilisers of facets in the Bruhat-Tits building.
Let us fix a Borel subgroup $B \subset G$, then for any parabolic subgroup $P \subset G$ that contains $B$, we can define the group $K_P$ as the set of $g \in G(O_F)$ such that the reduced element $\overline g$ lies in $P(O_F/\varpi_F)$.
My question: Is it true that any parahoric subgroup K of $G(F)$ is conjugate to one of the above groups $K_P$?