Subgroups — C₃⋊#21438962 #36384151

Order 22698.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16838253	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#21438962	—	3	1	no	maximal
3	C₁₃×D₂₉₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₉₇	C₂×C₃	1	1	yes	characteristic, complemented
5	#16838253	—	2	1	no	—
6	#16838253	D₃	1	1	yes	characteristic, complemented
7	C₁₃×D₉₇	—	3	1	no	Hall
8	C₃⋊(D₉₇⋊C₃)	—	13	1	no	maximal, Hall
9	C₁₃×C₉₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃×C₉₇⋊C₃	—	13	1	no	Hall
11	D₂₉₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented
12	D₉₇⋊C₃	—	39	1	no	—
13	C₃×C₉₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
14	C₉₇⋊C₃	—	13	1	no	—
15	C₉₇⋊C₃	—	26	1	no	—
16	D₃×C₁₃⋊C₃	—	97	1	no	maximal, Hall
17	D₉₇	—	3	1	no	Hall
18	C₃×C₁₃⋊C₃	—	97	1	no	Hall
19	C₉₇	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	D₃×C₁₃	—	97	1	no	—
21	C₂×C₁₃⋊C₃	—	291	1	no	—
22	C₃×C₁₃	D₉₇⋊C₃	1	1	yes	characteristic, complemented
23	C₁₃⋊C₃	—	97	1	no	—
24	C₁₃⋊C₃	—	194	1	no	—
25	C₂×C₁₃	—	291	1	no	Hall
26	C₃×D₃	—	1261	1	no	Hall
27	C₁₃	C₃⋊(D₉₇⋊C₃)	1	1	yes	characteristic, complemented, Sylow
28	C₃²	—	1261	1	no	Sylow
29	C₂×C₃	—	3783	1	no	—
30	D₃	—	97	1	no	—
31	C₃	—	2522	1	no	—
32	C₃	—	1261	1	no	—
33	C₃	#21438962	1	1	yes	characteristic, complemented
34	C₂	—	291	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₉₇	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₉₇
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.