Subgroups — (C₃⋊(C₃⋊C₁₆))⋊C₃ #88383

Order 432.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊C₁₆)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊C₁₆	—	3	1	no	maximal
4	C₄×H(3,𝔽₃)	C₄	1	1	yes	characteristic
5	C₃²×C₈	—	2	1	no	—
6	C₃²×C₈	D₃	1	1	yes	characteristic
7	C₃²×C₈	C₂×C₃	1	1	yes	characteristic
8	C₂×H(3,𝔽₃)	C₈	1	1	yes	characteristic
9	C₃×C₁₆	—	9	1	no	—
10	C₃⋊C₁₆	—	3	1	no	—
11	C₃⋊C₁₆	—	9	1	no	—
12	C₃²×C₄	—	2	1	no	—
13	C₃²×C₄	Dic₃	1	1	yes	characteristic
14	C₃²×C₄	C₃×C₄	1	1	yes	characteristic
15	H(3,𝔽₃)	C₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₃×C₈	—	3	1	no	—
17	C₃×C₈	—	3	1	no	—
18	C₃×C₈	—	6	1	no	—
19	C₃×C₈	C₃×D₃	1	1	yes	characteristic
20	C₂×C₃²	—	2	1	no	—
21	C₂×C₃²	C₃⋊C₈	1	1	yes	characteristic
22	C₂×C₃²	C₃×C₈	1	1	yes	characteristic
23	C₁₆	—	9	1	no	Sylow
24	C₃×C₄	—	3	1	no	—
25	C₃×C₄	—	3	1	no	—
26	C₃×C₄	—	6	1	no	—
27	C₃×C₄	C₃×Dic₃	1	1	yes	characteristic
28	C₃²	—	2	1	no	—
29	C₃²	C₃⋊C₁₆	1	1	yes	characteristic, complemented
30	C₃²	C₃×C₁₆	1	1	yes	characteristic, complemented
31	C₈	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
32	C₂×C₃	—	3	1	no	—
33	C₂×C₃	—	3	1	no	—
34	C₂×C₃	—	6	1	no	—
35	C₂×C₃	C₃×C₃⋊C₈	1	1	yes	characteristic
36	C₄	(C₃⋊Dic₃)⋊C₃	1	1	yes	characteristic
37	C₃	—	3	1	no	—
38	C₃	—	3	1	no	—
39	C₃	—	6	1	no	—
40	C₃	C₃×C₃⋊C₁₆	1	1	yes	characteristic
41	C₂	(C₃⋊(C₃⋊C₈))⋊C₃	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.