Abstract Dedicated to the memory of Jan Saxl Let $G$ be a finite primitive permutation group on set $\Omega $ with nontrivial point stabilizer $G_{\alpha }$. We say that is extremely if }$ acts primitively each its orbits in \setminus \{\alpha \}$. These groups arise naturally several different contexts, and their study can traced back work Manning 1920s. In this paper, we determine almost simp...