Subgroups — C₃⋊#24925159 #44569474

Order 32412.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₇₀₁	C₂	1	1	yes	maximal, characteristic
2	#24925159	—	3	1	no	maximal, Hall
3	C₃×C₃₇×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₂₇₀₁	D₃	1	1	yes	characteristic
5	C₃₇×C₇₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊#64408	—	37	1	no	maximal, Hall
7	C₃⋊#3866	—	73	1	no	maximal, Hall
8	C₃×D₇₃	—	37	1	no	—
9	#64408	—	111	1	no	Hall
10	C₃×D₃₇	—	73	1	no	—
11	C₃×C₇₃	#3866	1	1	yes	characteristic, complemented, Hall
12	#3866	—	219	1	no	Hall
13	D₇₃	—	37	1	no	—
14	C₃×C₃₇	#64408	1	1	yes	characteristic, complemented, Hall
15	D₃₇	—	73	1	no	—
16	C₇₃	C₃⋊#3866	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	C₃⋊#64408	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	2701	1	no	Hall
19	C₂×C₃	—	2701	1	no	—
20	C₄	—	8103	1	no	Sylow
21	C₃	#24925159	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	2701	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₃₇×C₇₃	C₄
prime radical, cosocle	C₃×D₂₇₀₁	C₂
LCS	G ▷ C₃×C₃₇×C₇₃
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.