Subgroups — A₄×C₃⋊D₃ #6330

Order 216.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃⋊D₃	C₃	1	1	yes	maximal, characteristic, complemented
3	D₃×A₄	—	3	4	no	maximal
4	C₃×C₃⋊D₃	—	4	1	no	maximal
5	C₂²×C₃²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×C₃⋊D₃	—	3	1	no	—
7	C₂×C₃⋊D₃	—	3	1	no	—
8	C₃×A₄	—	2	4	no	—
9	C₃×A₄	D₃	1	4	yes	complemented
10	C₃³	—	4	1	no	Sylow
11	C₂²×D₃	—	3	4	no	—
12	C₂×A₄	—	9	1	no	—
13	C₂×C₃²	—	3	1	no	—
14	C₃⋊D₃	—	3	1	no	—
15	C₃⋊D₃	A₄	1	1	yes	characteristic, direct product factor
16	C₃×D₃	—	12	4	no	—
17	C₂²×C₃	C₃×D₃	1	4	yes	complemented
18	C₂×D₃	—	9	4	no	—
19	C₂×D₃	—	9	4	no	—
20	A₄	—	2	4	no	—
21	A₄	C₃⋊D₃	1	1	yes	characteristic, direct product factor
22	C₃²	—	4	4	no	—
23	C₃²	—	8	4	no	—
24	C₃²	C₂×A₄	1	1	yes	characteristic, complemented
25	C₂³	—	9	1	no	Sylow
26	C₂×C₃	—	3	4	no	—
27	C₂×C₃	—	36	1	no	—
28	D₃	—	3	4	no	—
29	D₃	—	9	4	no	—
30	C₂²	—	27	1	no	—
31	C₂²	—	27	1	no	—
32	C₂²	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
33	C₃	—	4	1	no	—
34	C₃	—	8	4	no	—
35	C₃	D₃×A₄	1	4	yes	complemented
36	C₂	—	3	1	no	—
37	C₂	—	9	1	no	—
38	C₂	—	27	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₃²	C₂×C₃
LCS	G ▷ C₂²×C₃²
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.