Subgroups — D₇⋊C₉ #1252

Order 126.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₉	—	7	1	no	maximal, Hall
5	D₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₉	—	7	1	no	Sylow
7	C₇	C₂×C₉	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃	—	7	1	no	—
9	C₃	AGL(1,𝔽₇)	1	1	yes	characteristic
10	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₇	C₂×C₃
prime radical	C₃×D₇	C₃
LCS	G ▷ 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.