Subgroups — C₂×#1113 #6335

Order 216.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
2	#1113	C₂	1	4	yes	maximal, direct product factor
3	C₂×D₃²	—	3	3	no	maximal
4	C₂×C₃³	C₂²	1	1	yes	characteristic, complemented
5	C₃×C₃⋊D₃	C₂²	1	6	yes	complemented
6	C₂×C₃⋊D₃	D₃	1	3	yes	complemented
7	C₂×C₃×D₃	—	3	6	no	—
8	C₂×C₃×D₃	—	6	3	no	—
9	D₃²	—	3	12	no	—
10	C₃³	C₂³	1	1	yes	characteristic, complemented, Sylow
11	C₂²×D₃	—	9	3	no	—
12	C₂×C₃²	—	2	3	no	—
13	C₂×C₃²	—	4	1	no	—
14	C₂×C₃²	C₂×D₃	1	3	yes	complemented
15	C₃⋊D₃	C₂×D₃	1	6	yes	complemented
16	C₃×D₃	—	3	12	no	—
17	C₃×D₃	—	6	6	no	—
18	C₂²×C₃	—	9	3	no	—
19	C₂×D₃	—	3	6	no	—
20	C₂×D₃	—	6	3	no	—
21	C₂×D₃	—	9	12	no	—
22	C₃²	—	2	3	no	—
23	C₃²	—	4	1	no	—
24	C₃²	C₂²×D₃	1	3	yes	complemented
25	C₂³	—	27	1	no	Sylow
26	C₂×C₃	—	2	3	no	—
27	C₂×C₃	—	4	1	no	—
28	C₂×C₃	—	9	6	no	—
29	C₂×C₃	D₃²	1	3	yes	complemented
30	D₃	—	3	12	no	—
31	D₃	—	6	6	no	—
32	C₂²	—	9	3	no	—
33	C₂²	—	27	4	no	—
34	C₃	—	2	3	no	—
35	C₃	—	4	1	no	—
36	C₃	C₂×D₃²	1	3	yes	complemented
37	C₂	—	9	6	no	—
38	C₂	#1113	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#1113
commutator, cosocle, hypocenter	C₃³	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃³	C₂²
LCS	G ▷ C₃³
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.