Subgroups — C₃×Dic₁₁₃⋊C₇ #23748769

Order 9492.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁₃⋊C₇	C₂	1	1	yes	maximal, characteristic
2	Dic₁₁₃⋊C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁₃⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁₃⋊C₇	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₁₁₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₁₃⋊C₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₁₃	C₂×C₇	1	1	yes	characteristic
8	Dic₁₁₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₁₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁₃	C₂×C₃×C₇	1	1	yes	characteristic
11	C₁₁₃	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₇	—	113	1	no	maximal, Hall
13	C₂×C₃×C₇	—	113	1	no	—
14	C₄×C₇	—	113	1	no	Hall
15	C₃×C₇	—	113	1	no	Hall
16	C₂×C₇	—	113	1	no	—
17	C₃×C₄	—	113	1	no	Hall
18	C₇	—	113	1	no	Sylow
19	C₂×C₃	D₁₁₃⋊C₇	1	1	yes	characteristic
20	C₄	—	113	1	no	Sylow
21	C₃	Dic₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₁₁₃⋊C₇	1	1	yes	characteristic

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