Subgroups — C₃×Dic₁₃₅₁ #30633845

Order 16212.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₉₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₉₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₉₃	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₁₉₃	—	7	1	no	maximal, Hall
6	C₇×C₁₉₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₉₃	D₇	1	1	yes	characteristic
8	Dic₁₉₃	—	7	1	no	Hall
9	C₃×C₁₉₃	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₉₃	C₃×D₇	1	1	yes	characteristic
11	C₁₉₃	C₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
12	C₃×Dic₇	—	193	1	no	maximal, Hall
13	C₂×C₃×C₇	D₁₉₃	1	1	yes	characteristic
14	Dic₇	—	193	1	no	Hall
15	C₃×C₇	Dic₁₉₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇	C₃×D₁₉₃	1	1	yes	characteristic
17	C₃×C₄	—	1351	1	no	Hall
18	C₇	C₃×Dic₁₉₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₁₃₅₁	1	1	yes	characteristic
20	C₄	—	1351	1	no	Sylow
21	C₃	Dic₁₃₅₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₁₃₅₁	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.