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.
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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.