Subgroups — Dic₉₁ #67242

Order 364.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₃	—	7	1	no	maximal, Hall
4	Dic₇	—	13	1	no	maximal, Hall
5	C₂×C₁₃	D₇	1	1	yes	characteristic
6	C₂×C₇	D₁₃	1	1	yes	characteristic
7	C₁₃	Dic₇	1	1	yes	characteristic, complemented, Sylow
8	C₇	Dic₁₃	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	91	1	no	Sylow
10	C₂	D₉₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₉₁
commutator, hypocenter	C₇×C₁₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₁₃	C₂
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂

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.