Subgroups — #87648

Order 392.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇²	C₂	1	1	yes	maximal, characteristic
2	C₇⋊Dic₇	C₂	1	2	yes	maximal
3	C₂×C₇²	C₂²	1	1	yes	characteristic
4	Dic₁₄	—	7	8	no	maximal
5	C₇²	Q₈	1	1	yes	characteristic, complemented, Sylow
6	C₄×C₇	D₇	1	8	yes	—
7	Dic₇	—	7	16	no	—
8	C₂×C₇	C₂×D₇	1	8	yes	—
9	Q₈	—	49	1	no	Sylow
10	C₇	Dic₁₄	1	8	yes	complemented
11	C₄	—	49	2	no	—
12	C₄	C₇⋊D₇	1	1	yes	characteristic
13	C₂	C₂×C₇⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×C₇⋊D₇
commutator, socle, prime radical, cosocle	C₂×C₇²	C₂²
Fitting	C₄×C₇²	C₂
hypercenter	C₄	C₇⋊D₇
hypocenter	C₇²	Q₈
LCS	G ▷ C₂×C₇² ▷ C₇²
UCS	C₁ ◁ C₂ ◁ C₄

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₇²	Q₈	semidirect
10. C₇	Dic₁₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.