Subgroups — C₃⋊#622 #6281

Order 216.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	#622	—	3	1	no	maximal
3	C₂×C₃³	C₄	1	1	yes	characteristic
4	C₃⋊Dic₃	D₃	1	1	yes	characteristic
5	C₃×Dic₃	—	6	2	no	—
6	C₃³	C₈	1	1	yes	characteristic, complemented, Sylow
7	C₃⋊C₈	—	9	1	no	maximal
8	C₂×C₃²	—	2	2	no	—
9	C₂×C₃²	—	4	2	no	—
10	C₂×C₃²	Dic₃	1	1	yes	characteristic
11	C₃×C₄	—	9	1	no	—
12	Dic₃	—	6	2	no	—
13	C₃²	—	2	2	no	—
14	C₃²	—	4	2	no	—
15	C₃²	C₃⋊C₈	1	1	yes	characteristic, complemented
16	C₈	—	27	1	no	Sylow
17	C₂×C₃	—	2	2	no	—
18	C₂×C₃	—	4	2	no	—
19	C₂×C₃	#157	1	1	yes	characteristic
20	C₄	—	9	1	no	—
21	C₃	—	2	2	no	—
22	C₃	—	4	2	no	—
23	C₃	#622	1	1	yes	characteristic, complemented
24	C₂	C₃⋊#157	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#157
commutator, hypocenter	C₃³	C₈
Fitting, socle, prime radical	C₂×C₃³	C₄
cosocle	C₃×C₃⋊Dic₃	C₂
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.