Subgroups — C₄₇×Dic₃₇⋊C₃ #35229366

Order 20868.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₇×Dic₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₇×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×C₄₇	C₂×C₃	1	1	yes	characteristic
5	C₃₇×C₄₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₄₇	—	37	1	no	maximal, Hall
7	Dic₃₇⋊C₃	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₄₇	—	37	1	no	—
9	C₂×C₃₇⋊C₃	C₂×C₄₇	1	1	yes	characteristic
10	C₄×C₄₇	—	37	1	no	Hall
11	Dic₃₇	C₃×C₄₇	1	1	yes	characteristic, complemented, Hall
12	C₃×C₄₇	—	37	1	no	Hall
13	C₃₇⋊C₃	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₄₇	D₃₇⋊C₃	1	1	yes	characteristic
15	C₂×C₃₇	C₂×C₃×C₄₇	1	1	yes	characteristic
16	C₄₇	Dic₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₇	C₃×C₄×C₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	37	1	no	Hall
19	C₂×C₃	—	37	1	no	—
20	C₄	—	37	1	no	Sylow
21	C₃	—	37	1	no	Sylow
22	C₂	C₄₇×D₃₇⋊C₃	1	1	yes	characteristic

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.