It is well known that the maximal subalgebras of a semisimple Lie algebra g are certain semisimple subalgebras and the maximal parabolic subalgebras.This paper provides a classification of subalgebras h g such that every subalgebra strictly containing h is horospherical, i.e., contains a maximal unipotent subalgebra of g.
A. V. Smirnov (Mon,) studied this question.