Subgroups — C₃×Dic₂₀₃₃ #37567321

Order 24396.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₀₃₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₉×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₁₀₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₁₀₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₁₀₇	—	19	1	no	maximal, Hall
7	C₂×C₃×C₁₀₇	D₁₉	1	1	yes	characteristic
8	Dic₁₀₇	—	19	1	no	Hall
9	C₃×C₁₀₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
10	C₃×Dic₁₉	—	107	1	no	maximal, Hall
11	C₂×C₁₀₇	C₃×D₁₉	1	1	yes	characteristic
12	C₂×C₃×C₁₉	D₁₀₇	1	1	yes	characteristic
13	C₁₀₇	C₃×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
14	Dic₁₉	—	107	1	no	Hall
15	C₃×C₁₉	Dic₁₀₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₉	C₃×D₁₀₇	1	1	yes	characteristic
17	C₁₉	C₃×Dic₁₀₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2033	1	no	Hall
19	C₂×C₃	D₂₀₃₃	1	1	yes	characteristic
20	C₄	—	2033	1	no	Sylow
21	C₃	Dic₂₀₃₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₂₀₃₃	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.