On the normal subgroups and the factorization of some$\pi$-solvable irreducible linear groups

For finite $\pi$-solvable absolutely irreducible linear group of degree $n=2|H|$ over a field of zero characteristic with a $\pi$-Hall $TI$-subgroup $H$ of a odd order that is not normal, the existence of certain normal subgroups and factorizations is proved.