Normal reflection subgroups of an irreducible reflection group form a lattice combinatorially indexed by conjugacy orbits of root-line reflection subgroups, and every complex reflection group is normal in a unique maximal reflection group sharing its collineation group.
Discrete complex reflection groups
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Here are reproduced slightly edited notes of my lectures on the classification of discrete groups generated by complex reflections of Hermitian affine spaces delivered in October of 1980 at the University of Utrecht.
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The lattice of normal reflection subgroups of an irreducible reflection group
Normal reflection subgroups of an irreducible reflection group form a lattice combinatorially indexed by conjugacy orbits of root-line reflection subgroups, and every complex reflection group is normal in a unique maximal reflection group sharing its collineation group.