Subgroups — C₃⋊#157 #1110

Order 108.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃³	C₄
prime radical, cosocle	C₃×C₃⋊D₃	C₂
LCS	G ▷ C₃³
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.