Subgroups — C₂₃³ #27131582

Order 12167.

1108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃²	C₂₃	1	553	yes	maximal, direct product factor
2	C₂₃	C₂₃²	1	553	yes	direct product factor

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃²	C₂₃	direct (N × H)
2. C₂₃	C₂₃²	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃²	23