Subgroups — C₂×D₃² #649

Order 72.

69 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₃	C₂	1	2	yes	maximal, complemented
3	D₃²	C₂	1	4	yes	maximal, direct product factor
4	C₂²×D₃	—	3	2	no	maximal
5	C₂×C₃²	C₂²	1	1	yes	characteristic, complemented
6	C₃⋊D₃	C₂²	1	2	yes	complemented
7	C₃×D₃	C₂²	1	4	yes	complemented
8	C₂²×C₃	—	3	2	no	—
9	C₂×D₃	—	3	2	no	—
10	C₂×D₃	—	3	8	no	—
11	C₂×D₃	—	6	1	no	—
12	C₂×D₃	D₃	1	2	yes	direct product factor
13	C₃²	C₂³	1	1	yes	characteristic, complemented, Sylow
14	C₂³	—	9	1	no	Sylow
15	C₂×C₃	—	2	1	no	—
16	C₂×C₃	—	3	4	no	—
17	C₂×C₃	C₂×D₃	1	2	yes	complemented
18	D₃	—	3	4	no	—
19	D₃	—	6	2	no	—
20	D₃	C₂×D₃	1	4	yes	direct product factor
21	C₂²	—	3	2	no	—
22	C₂²	—	9	4	no	—
23	C₂²	—	9	1	no	—
24	C₃	—	2	1	no	—
25	C₃	C₂²×D₃	1	2	yes	complemented
26	C₂	—	3	4	no	—
27	C₂	—	9	2	no	—
28	C₂	D₃²	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃²
commutator, cosocle, hypocenter	C₃²	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃²	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂

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.