Subgroups — #92173

Order 486.

87 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6866	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊(C₃⋊D₃)	C₃	1	1	yes	maximal, characteristic
3	(C₃⋊D₃)⋊C₉	—	3	1	no	maximal
4	C₃⁴	C₂×C₃	1	1	yes	characteristic
5	C₃²⋊C₉	—	2	1	no	—
6	C₃²⋊C₉	D₃	1	1	yes	characteristic, complemented
7	C₃⋊(C₃⋊D₃)	C₉	1	1	yes	characteristic, complemented
8	C₃×C₃⋊D₃	—	3	1	no	—
9	C₃×C₃⋊D₃	—	9	1	no	—
10	C₃×C₃⋊D₃	—	9	3	no	—
11	D₃×C₉	—	9	1	no	—
12	C₃³	—	2	1	no	—
13	C₃³	—	3	3	no	—
14	C₃³	—	3	1	no	—
15	C₃³	—	6	1	no	—
16	C₃³	—	6	3	no	—
17	C₃³	C₂×C₉	1	1	yes	characteristic, complemented
18	C₃³	C₃×D₃	1	1	yes	characteristic
19	C₃×C₉	—	3	1	no	—
20	C₃×C₉	—	6	1	no	—
21	C₃⋊D₃	—	3	1	no	—
22	C₃⋊D₃	—	9	1	no	—
23	C₃⋊D₃	—	9	3	no	—
24	C₃×D₃	—	9	1	no	—
25	C₃×D₃	—	27	1	no	—
26	C₃×D₃	—	27	3	no	—
27	C₂×C₉	—	27	1	no	—
28	C₃²	—	2	1	no	—
29	C₃²	—	3	3	no	—
30	C₃²	—	3	1	no	—
31	C₃²	—	3	3	no	—
32	C₃²	—	3	1	no	—
33	C₃²	—	6	1	no	—
34	C₃²	—	6	3	no	—
35	C₃²	—	6	3	no	—
36	C₃²	—	6	3	no	—
37	C₃²	—	6	6	no	—
38	C₃²	—	6	1	no	—
39	C₃²	D₃×C₉	1	1	yes	characteristic
40	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
41	C₉	—	9	1	no	—
42	C₉	—	18	1	no	—
43	C₂×C₃	—	27	1	no	—
44	D₃	—	9	1	no	—
45	D₃	—	27	1	no	—
46	D₃	—	27	3	no	—
47	C₃	—	2	1	no	—
48	C₃	—	3	3	no	—
49	C₃	—	3	1	no	—
50	C₃	—	6	1	no	—
51	C₃	—	6	3	no	—
52	C₃	(C₃⋊D₃)⋊C₉	1	1	yes	characteristic
53	C₃	#4175	1	1	yes	characteristic
54	C₂	—	27	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.