Subgroups — C₃⋊(C₃⋊D₂₁) #67406

Order 378.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊D₂₁	—	3	13	no	maximal
3	C₃²×C₇	D₃	1	13	yes	complemented
4	C₃⋊(C₃⋊D₃)	—	7	1	no	maximal, Hall
5	D₂₁	—	9	13	no	—
6	C₃³	D₇	1	1	yes	characteristic, complemented, Sylow
7	C₃×C₇	C₃⋊D₃	1	13	yes	complemented
8	C₃⋊D₃	—	21	13	no	—
9	D₇	—	27	1	no	Hall
10	C₃²	D₂₁	1	13	yes	complemented
11	C₇	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented, Sylow
12	D₃	—	63	13	no	—
13	C₃	C₃⋊D₂₁	1	13	yes	complemented
14	C₂	—	189	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃³×C₇	C₂
LCS	G ▷ C₃³×C₇
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.