On factor-spaces of compact Lie groups by subgrops of co-rank one

Let $G$ be a compact connected Lie group, $L$ be a centralizer of torus in $G$, $H$ be the commutant of the group $L$, $\mathrm{cork}H=1$, $G/H$ be simply connected. We obtain the classification of transitive actions of compact Lie groups on the manifolds $G/H$.