Subgroups — #23751532⋊C₂ #34064483

Order 19306.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23751532	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₉₇	C₇	1	1	yes	maximal, characteristic
3	C₇×C₁₉₇	C₂×C₇	1	1	yes	characteristic
4	D₁₉₇	C₄₉	1	1	yes	characteristic, complemented, Hall
5	C₁₉₇	C₂×C₄₉	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₄₉	—	197	1	no	maximal, Hall
7	C₄₉	—	197	1	no	Sylow
8	C₂×C₇	—	197	1	no	—
9	C₇	D₁₉₇⋊C₇	1	1	yes	characteristic
10	C₂	—	197	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₇	D₁₉₇⋊C₇
commutator, hypocenter	C₁₉₇	C₂×C₄₉
Fitting, socle, cosocle	C₇×C₁₉₇	C₂×C₇
prime radical	C₇×D₁₉₇	C₇
LCS	G ▷ C₁₉₇
UCS	C₁ ◁ C₇

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.