Subgroups — C₃⋊(D₇⋊C₉) #67368

Order 378.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₂₁	C₃	1	1	yes	maximal, characteristic
3	D₇⋊C₉	—	3	1	no	maximal
4	C₃²×C₇	C₂×C₃	1	1	yes	characteristic
5	C₇⋊C₉	—	2	1	no	—
6	C₇⋊C₉	D₃	1	1	yes	characteristic, complemented
7	D₃×C₉	—	7	1	no	maximal, Hall
8	D₂₁	C₉	1	1	yes	characteristic, complemented
9	C₃×D₇	—	3	1	no	—
10	C₃×C₉	—	7	1	no	Sylow
11	C₃×C₇	—	2	1	no	—
12	C₃×C₇	C₂×C₉	1	1	yes	characteristic, complemented
13	C₃×C₇	C₃×D₃	1	1	yes	characteristic
14	C₃×D₃	—	7	1	no	—
15	C₂×C₉	—	21	1	no	—
16	D₇	—	3	1	no	Hall
17	C₃²	AGL(1,𝔽₇)	1	1	yes	characteristic
18	C₉	—	7	1	no	—
19	C₉	—	14	1	no	—
20	C₇	D₃×C₉	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃	—	21	1	no	—
22	D₃	—	7	1	no	—
23	C₃	—	2	1	no	—
24	C₃	D₇⋊C₉	1	1	yes	characteristic, complemented
25	C₃	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic
26	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₃⋊AGL(1,𝔽₇)
commutator, hypocenter	C₃×C₇	C₂×C₉
Fitting, socle, cosocle	C₃²×C₇	C₂×C₃
prime radical	C₃×D₂₁	C₃
LCS	G ▷ C₃×C₇
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.