Subgroups — C₃⋊#1088 #66421

Order 324.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#272	C₂	1	1	yes	maximal, characteristic
2	#1088	—	3	1	no	maximal
3	C₃×H(3,𝔽₃)	C₄	1	1	yes	characteristic, complemented, Sylow
4	C₃²×D₃	—	6	2	no	—
5	#272	D₃	1	1	yes	characteristic
6	C₃×Dic₃	—	9	1	no	maximal
7	C₃³	—	2	2	no	—
8	H(3,𝔽₃)	—	4	2	no	—
9	H(3,𝔽₃)	Dic₃	1	1	yes	characteristic, complemented
10	C₂×C₃²	—	9	1	no	—
11	C₃×D₃	—	6	2	no	—
12	C₃×D₃	—	6	2	no	—
13	C₃×D₃	—	6	4	no	—
14	C₃×C₄	—	27	1	no	—
15	Dic₃	—	9	1	no	—
16	C₃²	—	2	2	no	—
17	C₃²	—	4	2	no	—
18	C₃²	—	6	4	no	—
19	C₃²	—	6	2	no	—
20	C₃²	#157	1	1	yes	characteristic
21	C₂×C₃	—	9	1	no	—
22	C₂×C₃	—	9	1	no	—
23	C₂×C₃	—	18	1	no	—
24	D₃	—	6	2	no	—
25	C₄	—	27	1	no	Sylow
26	C₃	—	2	1	no	—
27	C₃	—	6	2	no	—
28	C₃	—	12	2	no	—
29	C₃	#1088	1	1	yes	characteristic, complemented
30	C₃	C₃⋊#157	1	1	yes	characteristic
31	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₃⋊#157
commutator, Fitting, hypocenter	C₃×H(3,𝔽₃)	C₄
socle	C₃²	#157
prime radical, cosocle	C₃×#272	C₂
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ 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.