Subgroups — C₉×D₁₇₁₇ #44525581

Order 30906.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₇₁₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₇×C₁₀₁	C₂×C₃	1	1	yes	characteristic
4	D₁₇₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₉×D₁₀₁	—	17	1	no	maximal, Hall
6	C₁₇×C₁₀₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₁₀₁	D₁₇	1	1	yes	characteristic, complemented, Hall
8	C₃×D₁₀₁	—	17	1	no	—
9	C₉×D₁₇	—	101	1	no	maximal, Hall
10	C₃×C₁₀₁	C₃×D₁₇	1	1	yes	characteristic
11	D₁₀₁	—	17	1	no	Hall
12	C₉×C₁₇	D₁₀₁	1	1	yes	characteristic, complemented, Hall
13	C₃×D₁₇	—	101	1	no	—
14	C₁₀₁	C₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₇	C₃×D₁₀₁	1	1	yes	characteristic
16	D₁₇	—	101	1	no	Hall
17	C₂×C₉	—	1717	1	no	Hall
18	C₁₇	C₉×D₁₀₁	1	1	yes	characteristic, complemented, Sylow
19	C₉	D₁₇₁₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	1717	1	no	—
21	C₃	C₃×D₁₇₁₇	1	1	yes	characteristic
22	C₂	—	1717	1	no	Sylow

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.