Subgroups — C₇×C₁₆ #1129

Order 112.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇	C₄	1	1	yes	characteristic
3	C₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₇	C₈	1	1	yes	characteristic
5	C₈	C₂×C₇	1	1	yes	characteristic
6	C₇	C₁₆	1	1	yes	characteristic, direct product factor, Sylow
7	C₄	C₄×C₇	1	1	yes	characteristic
8	C₂	C₇×C₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. C₁₆	C₇	direct (N × H)
6. C₇	C₁₆	direct (N × H)

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

subgroup	index
C₇×C₈	2
C₁₆	7