Subgroups — D₃×C₃⋊Dic₃ #6287

Order 216.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Maximal subgroups

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

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

Subgroups — D3×C3⋊Dic3 #6287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₃⋊Dic₃ #6287