Let
G
G
be a reductive algebraic group and let
Z
Z
be the stabilizer of a nilpotent element
e
e
of the Lie algebra of
G
G
. We consider the action of
Z
Z
on the flag variety of
G
G
, and we focus on the case where this action has a finite number of orbits (i.e.,
Z
Z
is a spherical subgroup). This holds for instance if
e
e
has height
2
2
. In this case we give a parametrization of the
Z
Z
-orbits and we show that each
Z
Z
-orbit has a structure of algebraic affine bundle. In particular, in type
A
A
, we deduce that each orbit has a natural cell decomposition. In the aim to study the (strong) Bruhat order of the orbits, we define an abstract partial order on certain quotients associated to a Coxeter system. In type
A
A
, we show that the Bruhat order of the
Z
Z
-orbits can be described in this way.