Subgroups — C₆₇⋊(C₁₁²⋊C₃) #37566583

Order 24321.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₆₇	—	3	4	no	—
3	C₁₁²⋊C₃	—	67	1	no	maximal, Hall
4	C₆₇⋊C₃	—	121	1	no	maximal, Hall
5	C₁₁²	C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
6	C₆₇	C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Sylow
7	C₁₁	—	3	4	no	—
8	C₃	—	8107	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₆₇	C₃
LCS	G ▷ C₁₁²×C₆₇
UCS	C₁

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

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