Critical $\Omega$-Fiber Formations of Finite Groups

Let $\mathfrak H$ be a class of finite groups. An $\Omega$-fiber formation $\mathfrak F$ of finite groups with direction $\varphi $ is said to be a minimal $\Omega$-fiber non-$\mathfrak H$-formation with direction $\varphi $, or briefly an $\mathfrak H_\Omega $-critical formation, if $\mathfrak F\nsubseteq \mathfrak H$, but any proper $\Omega$-fiber subformation with direction $\varphi $ in $\mathfrak F$ belongs to the class $\mathfrak H$. In the paper, a complete description of the structure of minimal $\Omega$-fiber non-$\mathfrak H$-formations of finite groups of two different directions is given.