Subgroups — C₃×C₇⋊(C₇⋊#261) #21439747

Order 7644.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₇⋊(C₇⋊#261)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇²×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₃×C₇⋊#261	—	7	8	no	maximal
6	C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇⋊Dic₇	—	13	1	no	maximal, Hall
8	C₃×C₇×D₁₃	D₇	1	8	yes	—
9	C₇⋊#261	—	7	8	no	—
10	C₂×C₃×C₇²	—	13	1	no	—
11	C₃×C₇×C₁₃	Dic₇	1	8	yes	complemented
12	C₇⋊Dic₇	—	13	1	no	Hall
13	C₇×D₁₃	C₃×D₇	1	8	yes	—
14	C₃×#261	—	49	1	no	Hall
15	C₃×C₇²	#261	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇²	—	13	1	no	—
17	C₇×C₁₃	C₃×Dic₇	1	8	yes	complemented
18	C₃×Dic₇	—	91	8	no	—
19	C₃×D₁₃	C₇⋊D₇	1	1	yes	characteristic
20	#261	—	49	1	no	Hall
21	C₇²	C₃×#261	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₇	—	13	8	no	—
23	C₃×C₁₃	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
24	Dic₇	—	91	8	no	—
25	D₁₃	C₃×C₇⋊D₇	1	1	yes	characteristic
26	C₃×C₇	C₇⋊#261	1	8	yes	complemented
27	C₂×C₇	—	13	8	no	—
28	C₁₃	C₃×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	637	1	no	Hall
30	C₇	C₃×C₇⋊#261	1	8	yes	complemented
31	C₂×C₃	—	13	1	no	—
32	C₄	—	637	1	no	Sylow
33	C₃	C₇⋊(C₇⋊#261)	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	13	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.