  We study the existence of projectable $G$-invariant Einstein metrics on the
total space of $G$-equivariant fibrations $M=G/L\to G/K$, for a compact
connected semisimple Lie group $G$. We obtain necessary conditions for the
existence of such Einstein metrics in terms of appropriate Casimir operators,
which is a generalization of the result by Wang and Ziller about Einstein
normal metrics. We describe binormal Einstein metrics which are the orthogonal
sum of the normal metrics on the fiber and on the base. The special case when
the restriction to the fiber and the projection to the base are also Einstein
is also considered. As an application, we prove the existence of a non-standard
Einstein invariant metric on the Kowalski $n$-symmetric spaces.
