Subgroups — Dic₃×C₃⋊D₃ #6288

Order 216.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃⋊D₃	—	3	1	no	maximal
5	D₃×Dic₃	—	3	4	no	maximal
6	C₂×C₃³	C₂²	1	1	yes	characteristic
7	C₃×C₃⋊D₃	C₄	1	2	yes	complemented
8	C₂×C₃⋊D₃	D₃	1	1	yes	characteristic
9	C₂×C₃×D₃	—	3	4	no	—
10	C₃²×C₄	—	3	1	no	—
11	C₃⋊Dic₃	—	3	1	no	—
12	C₃⋊Dic₃	—	3	4	no	—
13	C₃⋊Dic₃	—	6	4	no	—
14	C₃×Dic₃	D₃	1	4	yes	complemented
15	C₃³	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×Dic₃	—	9	1	no	—
17	C₄×D₃	—	9	4	no	—
18	C₂×C₃²	—	2	4	no	—
19	C₂×C₃²	C₂×D₃	1	4	yes	—
20	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
21	C₃⋊D₃	Dic₃	1	2	yes	direct product factor
22	C₃×D₃	—	3	8	no	—
23	C₂²×C₃	—	9	1	no	—
24	C₂×D₃	—	3	4	no	—
25	C₃×C₄	—	3	4	no	—
26	Dic₃	—	9	4	no	—
27	Dic₃	—	9	1	no	—
28	Dic₃	—	18	4	no	—
29	Dic₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
30	C₃²	—	2	4	no	—
31	C₃²	C₄×D₃	1	4	yes	complemented
32	C₃²	C₂×Dic₃	1	1	yes	characteristic, complemented
33	C₂×C₄	—	27	1	no	Sylow
34	C₂×C₃	—	2	4	no	—
35	C₂×C₃	—	9	2	no	—
36	C₂×C₃	D₃²	1	4	yes	—
37	C₂×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
38	D₃	—	3	8	no	—
39	C₂²	—	9	1	no	—
40	C₄	—	3	1	no	—
41	C₄	—	27	1	no	—
42	C₃	—	2	4	no	—
43	C₃	D₃×Dic₃	1	4	yes	complemented
44	C₃	C₄×C₃⋊D₃	1	1	yes	characteristic, complemented
45	C₂	—	9	2	no	—
46	C₂	D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₃⋊D₃
commutator, hypocenter	C₃³	C₂×C₄
Fitting, socle, cosocle	C₂×C₃³	C₂²
prime radical	C₂×C₃×C₃⋊D₃	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃⋊(C₃⋊Dic₃)	C₂	semidirect
3. C₃²×Dic₃	C₂	semidirect
7. C₃×C₃⋊D₃	C₄	semidirect
14. C₃×Dic₃	D₃	semidirect
15. C₃³	C₂×C₄	semidirect
21. C₃⋊D₃	Dic₃	direct (N × H)
29. Dic₃	C₃⋊D₃	direct (N × H)
31. C₃²	C₄×D₃	semidirect
32. C₃²	C₂×Dic₃	semidirect
43. C₃	D₃×Dic₃	semidirect
44. C₃	C₄×C₃⋊D₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₃⋊D₃	2
C₃⋊(C₃⋊Dic₃)	2
C₃²×Dic₃	2
C₄×C₃⋊D₃	3
D₃×Dic₃	3

Subgroups — Dic3×C3⋊D3 #6288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×C₃⋊D₃ #6288