Subgroups — C₃⋊D₂₇ #4182

Order 162.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊D₉	—	3	1	no	maximal
3	D₂₇	—	3	3	no	maximal
4	C₃×C₉	D₃	1	1	yes	characteristic
5	C₂₇	D₃	1	3	yes	complemented
6	C₃⋊D₃	—	9	1	no	—
7	D₉	—	9	2	no	—
8	D₉	—	9	1	no	—
9	C₃²	D₉	1	1	yes	characteristic
10	C₉	D₉	1	2	yes	—
11	C₉	C₃⋊D₃	1	1	yes	characteristic
12	D₃	—	27	3	no	—
13	D₃	—	27	1	no	—
14	C₃	D₂₇	1	3	yes	complemented
15	C₃	C₃⋊D₉	1	1	yes	characteristic
16	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₂₇	C₂
Frattini	C₉	C₃⋊D₃
socle	C₃²	D₉
LCS	G ▷ C₃×C₂₇
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.