Subgroups — C₄⋊AGL(1,ℤ/9) #6217

Order 216.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
2	C₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₂	—	3	1	no	maximal
4	D₃₆	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×3₋¹⁺²	C₂²	1	1	yes	characteristic
6	AGL(1,ℤ/9)	—	2	2	no	—
7	C₂×C₃×D₃	—	3	2	no	—
8	C₃²×C₄	D₃	1	1	yes	characteristic
9	C₂×D₉	C₂×C₃	1	2	yes	complemented
10	C₄×C₉	—	2	1	no	—
11	C₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
12	3₋¹⁺²	D₄	1	1	yes	characteristic, complemented, Sylow
13	C₃×D₄	—	9	1	no	—
14	D₁₂	—	3	1	no	—
15	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
16	C₃×D₃	—	6	2	no	—
17	C₂×C₉	—	2	1	no	—
18	C₂×C₉	C₂²×C₃	1	1	yes	characteristic
19	D₉	—	2	2	no	—
20	C₂²×C₃	—	9	2	no	—
21	C₂×D₃	—	3	2	no	—
22	C₃×C₄	—	3	1	no	—
23	C₃×C₄	C₃×D₃	1	1	yes	characteristic
24	C₃²	D₁₂	1	1	yes	characteristic
25	C₉	—	2	1	no	—
26	C₉	C₃×D₄	1	1	yes	characteristic, complemented
27	D₄	—	9	1	no	Sylow
28	C₂×C₃	—	3	1	no	—
29	C₂×C₃	—	18	2	no	—
30	C₂×C₃	C₂×C₃×D₃	1	1	yes	characteristic
31	D₃	—	6	2	no	—
32	C₂²	—	9	2	no	—
33	C₄	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
34	C₃	—	3	1	no	—
35	C₃	C₃×D₁₂	1	1	yes	characteristic
36	C₂	—	18	2	no	—
37	C₂	C₂×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.