Subgroups — C₃×C₄×C₃₃₇⋊C₇ #43246705

Order 28308.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₃₇⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃₃₇⋊C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₃₃₇⋊C₇	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃₃₇⋊C₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₃₃₇	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃₃₇⋊C₇	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₃₃₇	C₂×C₇	1	1	yes	characteristic
8	C₄×C₃₃₇	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₃₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃₃₇	C₂×C₃×C₇	1	1	yes	characteristic
11	C₃₃₇	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₇	—	337	1	no	maximal, Hall
13	C₂×C₃×C₇	—	337	1	no	—
14	C₄×C₇	—	337	1	no	Hall
15	C₃×C₇	—	337	1	no	Hall
16	C₂×C₇	—	337	1	no	—
17	C₃×C₄	C₃₃₇⋊C₇	1	1	yes	characteristic, direct product factor, Hall
18	C₇	—	337	1	no	Sylow
19	C₂×C₃	C₂×C₃₃₇⋊C₇	1	1	yes	characteristic
20	C₄	C₃×C₃₃₇⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₄×C₃₃₇⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₃₃₇⋊C₇	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.