Subgroups — C₉×#14583753 #37613607

Order 24804.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₆₈₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#14583753	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×D₆₈₉	C₂×C₃	1	1	yes	characteristic
5	#14583753	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₃×C₅₃	C₃×C₄	1	1	yes	characteristic
7	C₉×#6157	—	13	1	no	maximal, Hall
8	D₆₈₉	C₂×C₉	1	1	yes	characteristic
9	C₉×D₅₃	—	13	1	no	—
10	C₁₃×C₅₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×#6157	—	13	1	no	—
12	C₉×C₅₃	#261	1	1	yes	characteristic, complemented, Hall
13	C₉×#261	—	53	1	no	maximal, Hall
14	C₃×D₅₃	—	13	1	no	—
15	C₉×D₁₃	—	53	1	no	—
16	#6157	—	13	1	no	Hall
17	C₃×C₅₃	C₃×#261	1	1	yes	characteristic
18	C₃×#261	—	53	1	no	—
19	C₉×C₁₃	#6157	1	1	yes	characteristic, complemented, Hall
20	D₅₃	—	13	1	no	—
21	C₃×D₁₃	—	53	1	no	—
22	C₅₃	C₉×#261	1	1	yes	characteristic, complemented, Sylow
23	#261	—	53	1	no	Hall
24	C₃×C₁₃	C₃×#6157	1	1	yes	characteristic
25	C₄×C₉	—	689	1	no	Hall
26	D₁₃	—	53	1	no	—
27	C₂×C₉	—	689	1	no	—
28	C₁₃	C₉×#6157	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	689	1	no	—
30	C₉	#14583753	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	689	1	no	—
32	C₄	—	689	1	no	Sylow
33	C₃	C₃×#14583753	1	1	yes	characteristic
34	C₂	—	689	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.