Subgroups — C₉×#272 #92298

Order 486.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×#272	C₃	1	1	yes	maximal, characteristic
3	C₃×D₃×C₉	—	3	4	no	maximal
4	C₃×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
5	C₃²×C₉	D₃	1	4	yes	complemented
6	C₃²⋊C₉	—	2	4	no	—
7	C₃²×D₃	—	3	4	no	—
8	C₂×C₃×C₉	—	9	1	no	—
9	#272	C₉	1	1	yes	characteristic, direct product factor
10	D₃×C₉	—	3	12	no	—
11	C₃³	C₃×D₃	1	4	yes	—
12	H(3,𝔽₃)	—	2	4	no	—
13	H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
14	C₃×C₉	—	2	4	no	—
15	C₃×C₉	—	3	12	no	—
16	C₃×C₉	C₃⋊D₃	1	1	yes	characteristic
17	C₂×C₃²	—	9	1	no	—
18	C₃×D₃	—	3	4	no	—
19	C₃×D₃	—	3	8	no	—
20	C₃×D₃	—	3	4	no	—
21	C₂×C₉	—	9	3	no	—
22	C₃²	—	2	4	no	—
23	C₃²	—	3	4	no	—
24	C₃²	—	3	8	no	—
25	C₃²	D₃×C₉	1	4	yes	complemented
26	C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
27	C₉	—	6	4	no	—
28	C₉	#272	1	3	yes	direct product factor
29	C₂×C₃	—	9	1	no	—
30	C₂×C₃	—	9	1	no	—
31	C₂×C₃	—	9	2	no	—
32	D₃	—	3	4	no	—
33	C₃	—	3	4	no	—
34	C₃	—	6	4	no	—
35	C₃	C₉×C₃⋊D₃	1	1	yes	characteristic
36	C₃	C₃×#272	1	1	yes	characteristic
37	C₃	#4208	1	2	yes	—
38	C₂	—	9	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.