Subgroups — C₉×C₂₃⋊#595 #28381007

Order 14076.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₃⋊#595	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₇×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×D₁₇	C₂×C₃	1	1	yes	characteristic
5	C₂₃⋊#595	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₇×C₂₃	C₃×C₄	1	1	yes	characteristic
7	C₉×Dic₂₃	—	17	1	no	maximal, Hall
8	C₂₃×D₁₇	C₂×C₉	1	1	yes	characteristic
9	C₉×#595	—	23	1	no	maximal, Hall
10	C₂×C₉×C₂₃	—	17	1	no	—
11	C₁₇×C₂₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₉×D₁₇	D₂₃	1	1	yes	characteristic
13	C₃×Dic₂₃	—	17	1	no	—
14	C₉×C₂₃	#595	1	1	yes	characteristic, complemented, Hall
15	C₃×#595	—	23	1	no	—
16	C₉×C₁₇	Dic₂₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₂₃	—	17	1	no	—
18	C₃×D₁₇	C₃×D₂₃	1	1	yes	characteristic
19	Dic₂₃	—	17	1	no	Hall
20	C₃×C₂₃	C₃×#595	1	1	yes	characteristic
21	#595	—	23	1	no	Hall
22	C₃×C₁₇	C₃×Dic₂₃	1	1	yes	characteristic
23	C₂×C₂₃	—	17	1	no	—
24	C₄×C₉	—	391	1	no	Hall
25	D₁₇	C₉×D₂₃	1	1	yes	characteristic
26	C₂₃	C₉×#595	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	17	1	no	—
28	C₁₇	C₉×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	391	1	no	—
30	C₉	C₂₃⋊#595	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	17	1	no	—
32	C₄	—	391	1	no	Sylow
33	C₃	C₃×C₂₃⋊#595	1	1	yes	characteristic
34	C₂	—	17	1	no	—

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.