Subgroups — D₉×H(3,𝔽₃) #92254

Order 486.

100 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	D₃×H(3,𝔽₃)	—	3	1	no	maximal
3	C₃²×D₉	C₃	1	4	yes	maximal, complemented
4	C₃×H(3,𝔽₃)	D₃	1	1	yes	characteristic
5	C₃²×C₉	C₂×C₃	1	4	yes	complemented
6	C₃²⋊C₉	—	2	4	no	—
7	C₃²×D₃	—	3	4	no	—
8	C₂×H(3,𝔽₃)	—	9	1	no	—
9	C₃×D₉	—	3	4	no	—
10	C₃×D₉	C₃²	1	1	yes	characteristic
11	C₃³	C₃×D₃	1	4	yes	—
12	H(3,𝔽₃)	—	2	4	no	—
13	H(3,𝔽₃)	D₉	1	1	yes	characteristic, direct product factor
14	C₃×C₉	—	2	4	no	—
15	C₃×C₉	—	3	4	no	—
16	C₃×C₉	—	6	4	no	—
17	C₃×C₉	C₂×C₃²	1	1	yes	characteristic
18	C₂×C₃²	—	9	4	no	—
19	C₃×D₃	—	3	1	no	—
20	C₃×D₃	—	9	4	no	—
21	D₉	H(3,𝔽₃)	1	1	yes	characteristic, direct product factor
22	C₃²	—	2	4	no	—
23	C₃²	—	3	4	no	—
24	C₃²	—	6	4	no	—
25	C₃²	C₃×D₉	1	4	yes	complemented
26	C₃²	C₃²×D₃	1	1	yes	characteristic
27	C₉	—	2	1	no	—
28	C₉	—	6	4	no	—
29	C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
30	C₂×C₃	—	9	1	no	—
31	C₂×C₃	—	27	4	no	—
32	D₃	—	3	1	no	—
33	C₃	—	2	1	no	—
34	C₃	—	3	4	no	—
35	C₃	—	6	4	no	—
36	C₃	C₃²×D₉	1	1	yes	characteristic
37	C₃	D₃×H(3,𝔽₃)	1	1	yes	characteristic
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.