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I'm trying to find normal subgroups of the symmetry group of the cube, the one with the 48 matrices. Apparently there are 9 normal subgroups. I've found like 4, the obvious ones: the identity, the whole group itself, the kernel and the centre. (Maybe the ker(determinant) also?) How can I go about finding the others? Any hints? I was thinking about intersections but the order of the groups are throwing me off.

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closed as off-topic by Shailesh, Leucippus, Claude Leibovici, 5xum, Robert Z Nov 16 '17 at 9:31

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Hint: Intersection of two normal subgroups is normal

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