Subgroups — C₃⋊(3₋¹⁺²⋊C₄) #66408

Order 324.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊Dic₃	—	3	1	no	maximal
3	C₃⋊Dic₉	C₃	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²⋊C₄	—	3	3	no	maximal
5	C₃×3₋¹⁺²	C₄	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃³	D₃	1	1	yes	characteristic
7	C₂×3₋¹⁺²	—	2	3	no	—
8	C₂×3₋¹⁺²	D₃	1	3	yes	—
9	C₂×C₃×C₉	—	2	1	no	—
10	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
11	C₃⋊Dic₃	—	3	1	no	—
12	C₃×Dic₃	—	9	3	no	—
13	C₃×Dic₃	—	9	1	no	—
14	Dic₉	—	3	3	no	—
15	C₃³	Dic₃	1	1	yes	characteristic
16	3₋¹⁺²	—	2	3	no	—
17	3₋¹⁺²	Dic₃	1	3	yes	complemented
18	C₃×C₉	—	2	1	no	—
19	C₃×C₉	C₃×C₄	1	1	yes	characteristic, complemented
20	C₂×C₃²	—	2	1	no	—
21	C₂×C₃²	—	3	3	no	—
22	C₂×C₃²	C₃×D₃	1	1	yes	characteristic
23	C₂×C₃²	C₃⋊D₃	1	1	yes	characteristic
24	C₂×C₉	—	2	3	no	—
25	C₂×C₉	C₃×D₃	1	3	yes	—
26	C₃×C₄	—	27	1	no	—
27	Dic₃	—	9	3	no	—
28	Dic₃	—	9	1	no	—
29	C₃²	—	2	1	no	—
30	C₃²	—	3	3	no	—
31	C₃²	C₃×Dic₃	1	1	yes	characteristic
32	C₃²	C₃⋊Dic₃	1	1	yes	characteristic
33	C₉	—	2	3	no	—
34	C₉	C₃×Dic₃	1	3	yes	complemented
35	C₂×C₃	—	3	1	no	—
36	C₂×C₃	—	6	1	no	—
37	C₂×C₃	AGL(1,ℤ/9)	1	3	yes	—
38	C₂×C₃	C₃×C₃⋊D₃	1	1	yes	characteristic
39	C₄	—	27	1	no	Sylow
40	C₃	—	3	1	no	—
41	C₃	—	6	1	no	—
42	C₃	3₋¹⁺²⋊C₄	1	3	yes	complemented
43	C₃	C₃×C₃⋊Dic₃	1	1	yes	characteristic
44	C₂	C₃⋊AGL(1,ℤ/9)	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.