Subgroups — Dic₃₆⋊C₃ #88472

Order 432.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²⋊Q₈	C₂	1	2	yes	maximal
2	C₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
3	C₃×Dic₁₂	—	3	1	no	maximal
4	Dic₃₆	C₃	1	1	yes	maximal, characteristic, complemented
5	C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
6	3₋¹⁺²⋊C₄	—	2	2	no	—
7	C₃×Dic₆	—	3	2	no	—
8	C₃²×C₈	D₃	1	1	yes	characteristic
9	Dic₁₈	C₂×C₃	1	2	yes	—
10	C₈×C₉	—	2	1	no	—
11	C₈×C₉	C₂×C₃	1	1	yes	characteristic
12	C₂×3₋¹⁺²	D₄	1	1	yes	characteristic
13	C₃×Q₁₆	—	9	1	no	—
14	Dic₁₂	—	3	1	no	—
15	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
16	C₃×Dic₃	—	6	2	no	—
17	C₄×C₉	—	2	1	no	—
18	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
19	Dic₉	—	2	2	no	—
20	3₋¹⁺²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₃×Q₈	—	9	2	no	—
22	Dic₆	—	3	2	no	—
23	C₃×C₈	—	6	1	no	—
24	C₃×C₈	C₃×D₃	1	1	yes	characteristic
25	C₂×C₃²	D₁₂	1	1	yes	characteristic
26	C₂×C₉	—	2	1	no	—
27	C₂×C₉	C₃×D₄	1	1	yes	characteristic
28	Q₁₆	—	9	1	no	Sylow
29	C₃×C₄	—	6	1	no	—
30	C₃×C₄	—	18	2	no	—
31	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
32	Dic₃	—	6	2	no	—
33	C₃²	Dic₁₂	1	1	yes	characteristic
34	C₉	—	2	1	no	—
35	C₉	C₃×Q₁₆	1	1	yes	characteristic, complemented
36	Q₈	—	9	2	no	—
37	C₈	AGL(1,ℤ/9)	1	1	yes	characteristic
38	C₂×C₃	—	6	1	no	—
39	C₂×C₃	C₃×D₁₂	1	1	yes	characteristic
40	C₄	—	18	2	no	—
41	C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
42	C₃	—	6	1	no	—
43	C₃	C₃×Dic₁₂	1	1	yes	characteristic
44	C₂	C₄⋊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.