Subgroups — C₃⋊#16864281 #27166166

Order 12876.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₀₇₃	C₂	1	1	yes	maximal, characteristic
2	#16864281	—	3	1	no	maximal, Hall
3	C₃×C₂₉×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₀₇₃	D₃	1	1	yes	characteristic
5	C₂₉×C₃₇	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊#3866	—	29	1	no	maximal, Hall
7	C₃⋊#1181	—	37	1	no	maximal, Hall
8	C₃×D₃₇	—	29	1	no	—
9	C₃×D₂₉	—	37	1	no	—
10	#3866	—	87	1	no	Hall
11	#1181	—	111	1	no	Hall
12	C₃×C₃₇	#1181	1	1	yes	characteristic, complemented, Hall
13	C₃×C₂₉	#3866	1	1	yes	characteristic, complemented, Hall
14	D₃₇	—	29	1	no	—
15	D₂₉	—	37	1	no	—
16	C₃₇	C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	C₃⋊#3866	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	1073	1	no	Hall
19	C₂×C₃	—	1073	1	no	—
20	C₄	—	3219	1	no	Sylow
21	C₃	#16864281	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	1073	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₂₉×C₃₇	C₄
prime radical, cosocle	C₃×D₁₀₇₃	C₂
LCS	G ▷ C₃×C₂₉×C₃₇
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.