Subgroups — #13047066

Order 1296.

113 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₉⋊D₉	C₂	1	1	yes	maximal, characteristic
2	#10619526	C₂	1	2	yes	maximal, complemented
3	C₂×C₉⋊D₉	C₄	1	1	yes	characteristic
4	C₄×C₉²	C₄	1	1	yes	characteristic
5	C₉⋊Dic₉	C₂²	1	1	yes	characteristic
6	C₄×C₃⋊D₉	—	6	2	no	—
7	C₂×C₉²	C₂×C₄	1	1	yes	characteristic
8	C₉⋊D₉	C₈	1	2	yes	complemented
9	#3787	—	9	1	no	maximal
10	C₂×C₃⋊D₉	—	6	2	no	—
11	C₃×C₄×C₉	—	2	2	no	—
12	C₃⋊Dic₉	—	6	2	no	—
13	C₉²	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
14	C₄×C₃⋊D₃	—	9	1	no	—
15	#622	—	9	2	no	—
16	C₄×D₉	—	18	6	no	—
17	C₂×C₃×C₉	—	2	2	no	—
18	C₃⋊D₉	—	6	4	no	—
19	C₂×C₃⋊D₃	—	9	1	no	—
20	C₃²×C₄	#157	1	1	yes	characteristic
21	C₃⋊Dic₃	—	9	1	no	—
22	C₂×D₉	—	18	6	no	—
23	C₄×C₉	—	2	6	no	—
24	Dic₉	—	18	6	no	—
25	C₃×C₉	—	2	2	no	—
26	C₄×D₃	—	54	2	no	—
27	C₂×C₃²	C₂×#157	1	1	yes	characteristic
28	C₃⋊D₃	—	9	2	no	—
29	C₂×C₉	—	2	6	no	—
30	D₉	—	18	12	no	—
31	C₂×C₈	—	81	1	no	Sylow
32	C₂×D₃	—	54	2	no	—
33	C₃×C₄	—	2	2	no	—
34	Dic₃	—	54	2	no	—
35	C₃²	#3787	1	1	yes	characteristic
36	C₉	—	2	6	no	—
37	C₂×C₄	—	81	1	no	—
38	C₈	—	81	2	no	—
39	C₂×C₃	—	2	2	no	—
40	D₃	—	54	4	no	—
41	C₂²	—	81	1	no	—
42	C₄	—	81	1	no	—
43	C₄	#66343	1	1	yes	characteristic
44	C₃	—	2	2	no	—
45	C₂	—	81	2	no	—
46	C₂	C₂×#66343	1	1	yes	characteristic

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.