Subgroups — #5997⋊C₂ #87657

Order 392.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇²	C₂	1	2	yes	maximal, complemented
2	#5997	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊D₇	C₂²	1	1	yes	characteristic
4	C₇×D₇	—	2	2	no	—
5	C₇²	D₄	1	1	yes	characteristic, complemented, Sylow
6	C₂×D₇	—	14	2	no	—
7	C₂×C₇	—	14	2	no	—
8	D₇	—	2	2	no	—
9	D₇	—	14	2	no	—
10	D₇	—	28	1	no	—
11	D₄	—	49	1	no	maximal, Sylow
12	C₇	—	2	2	no	—
13	C₇	—	4	1	no	—
14	C₂²	—	49	2	no	—
15	C₄	—	49	1	no	—
16	C₂	—	14	2	no	—
17	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₇⋊D₇	C₂²
Fitting, socle, hypocenter	C₇²	D₄
LCS	G ▷ C₇⋊D₇ ▷ C₇²
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.