Subgroups — C₂×C₃×C₃⋊D₃ #1116

Order 108.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃³	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₃

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.