Short exact sequence of groups schemes and dimensions

Question

Let $G$ be a projective groups scheme over an algebraically closed field of positive characteristic $p$. Denote by $G_t$ the $p$-torsion part of $G$ i.e., elements $g \in G$ such that $g^p=0$. Is there any relation between the dimensions of $G$, $G_t$ and $G/G_t$? In particular, is $\dim(G/G_t)=\dim G-\dim G_t$?