  Let $\mathfrak{X}$ be a class of finite groups closed under subgroups,
homomorphic images, and extensions. We study the question which goes back to
the lectures of H. Wielandt in 1963-64: For a given $\mathfrak{X}$-subgroup $K$
and maximal $\mathfrak{X}$-subgroup $H$, is it possible to see embeddability of
$K$ in $H$ (up to conjugacy) by their projections onto the factors of a fixed
subnormal series. On the one hand, we construct examples where $K$ has the same
projections as some subgroup of $H$ but is not conjugate to any subgroup of
$H$. On the other hand, we prove that if $K$ normalizes the projections of a
subgroup $H$, then $K$ is conjugate to a subgroup of $H$ even in the more
general case when $H$ is a submaximal $\mathfrak{X}$-subgroup.
