Subgroups — 3₋¹⁺²⋊D₇ #67386

Order 378.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₂₁	—	3	1	no	maximal
3	D₆₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₇	D₃	1	1	yes	characteristic
5	C₇×C₉	—	2	1	no	—
6	C₇×C₉	C₂×C₃	1	1	yes	characteristic, complemented
7	AGL(1,ℤ/9)	—	7	1	no	maximal, Hall
8	D₂₁	—	3	1	no	—
9	C₃×D₇	—	9	1	no	—
10	3₋¹⁺²	D₇	1	1	yes	characteristic, complemented, Sylow
11	C₃×C₇	—	3	1	no	—
12	C₃×C₇	C₃×D₃	1	1	yes	characteristic
13	C₃×D₃	—	21	1	no	—
14	D₉	—	7	1	no	—
15	D₇	—	9	1	no	Hall
16	C₃²	D₂₁	1	1	yes	characteristic
17	C₉	—	2	1	no	—
18	C₉	C₃×D₇	1	1	yes	characteristic, complemented
19	C₇	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	63	1	no	—
21	D₃	—	21	1	no	—
22	C₃	—	3	1	no	—
23	C₃	C₃×D₂₁	1	1	yes	characteristic
24	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₇×C₉	C₂×C₃
Frattini	C₃	C₃×D₂₁
Fitting	C₇×3₋¹⁺²	C₂
socle	C₃×C₇	C₃×D₃
LCS	G ▷ C₇×C₉
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.