Subgroups — C₃²×D₃₇₁ #20269254

Order 6678.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₃₇₁	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₅₃	C₂×C₃	1	4	yes	complemented
4	C₃²×D₅₃	—	7	1	no	maximal, Hall
5	D₃₇₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₅₃	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₅₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×D₅₃	—	7	4	no	—
9	C₃×C₅₃	C₃×D₇	1	4	yes	complemented
10	C₃²×D₇	—	53	1	no	maximal, Hall
11	D₅₃	—	7	1	no	Hall
12	C₃²×C₇	D₅₃	1	1	yes	characteristic, complemented, Hall
13	C₅₃	C₃²×D₇	1	1	yes	characteristic, complemented, Sylow
14	C₃×D₇	—	53	4	no	—
15	C₃×C₇	C₃×D₅₃	1	4	yes	complemented
16	C₂×C₃²	—	371	1	no	Hall
17	D₇	—	53	1	no	Hall
18	C₃²	D₃₇₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₇	C₃²×D₅₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	371	4	no	—
21	C₃	C₃×D₃₇₁	1	4	yes	direct product factor
22	C₂	—	371	1	no	Sylow

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