Subgroups — C₃⋊#27134418 #49147367

Order 36924.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃₀₇₇	C₂	1	1	yes	maximal, characteristic
2	#27134418	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₁₈₁	C₄	1	1	yes	characteristic, complemented, Hall
4	D₃₀₇₇	D₃	1	1	yes	characteristic
5	C₁₇×C₁₈₁	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊#10624382	—	17	1	no	maximal, Hall
7	C₃×D₁₈₁	—	17	1	no	—
8	#10624382	—	51	1	no	Hall
9	C₃×C₁₈₁	#595	1	1	yes	characteristic, complemented, Hall
10	D₁₈₁	—	17	1	no	—
11	C₃⋊#595	—	181	1	no	maximal, Hall
12	C₁₈₁	C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
13	C₃×D₁₇	—	181	1	no	—
14	#595	—	543	1	no	Hall
15	C₃×C₁₇	#10624382	1	1	yes	characteristic, complemented, Hall
16	D₁₇	—	181	1	no	—
17	C₁₇	C₃⋊#10624382	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	3077	1	no	Hall
19	C₂×C₃	—	3077	1	no	—
20	C₄	—	9231	1	no	Sylow
21	C₃	#27134418	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3077	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₇×C₁₈₁	C₄
prime radical, cosocle	C₃×D₃₀₇₇	C₂
LCS	G ▷ C₃×C₁₇×C₁₈₁
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.