Subgroups — D₃×C₃⋊D₃ #1112

Order 108.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃³	C₂²
LCS	G ▷ C₃³
UCS	C₁

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.