Subgroups — #20297117⋊C₃ #36319587

Order 21372.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₃⋊C₃)⋊D₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#20297117	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₇₈₁	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₃₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#10587739	—	13	1	no	maximal, Hall
7	C₃×D₁₃₇	—	13	1	no	—
8	#10587739	—	13	1	no	Hall
9	C₃×C₁₃₇	—	52	1	no	Hall
10	D₁₃₇	—	13	1	no	—
11	AGL(1,𝔽₁₃)	—	137	1	no	maximal, Hall
12	C₁₃₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
13	D₁₃⋊C₃	—	137	1	no	—
14	#261	—	137	1	no	Hall
15	C₁₃⋊C₃	#10587739	1	1	yes	characteristic, complemented, Hall
16	D₁₃	—	137	1	no	—
17	C₁₃	C₃×#10587739	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1781	1	no	Hall
19	C₂×C₃	—	1781	1	no	—
20	C₄	—	1781	1	no	Sylow
21	C₃	—	13	1	no	Sylow
22	C₂	—	1781	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₃₇	C₃×C₄
prime radical	(C₁₃⋊C₃)⋊D₁₃₇	C₂
cosocle	D₁₇₈₁	C₂×C₃
LCS	G ▷ C₁₃×C₁₃₇
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.