Parabolic subgroups of quaternionic reflection groups lack complements in their normalizers in general, with infinitely many examples in rank >2 and a complete classification for irreducible groups.
Du Val, Homographies, quaternions and rotations
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On Normalizers of Parabolic Subgroups of Quaternionic Reflection Groups
Parabolic subgroups of quaternionic reflection groups lack complements in their normalizers in general, with infinitely many examples in rank >2 and a complete classification for irreducible groups.