Finite Group Databasebeta

← C₂×C₇×C₇₆₉ #24924598

Subgroups — C₂×C₇×C₇₆₉ #24924598

Order 10766.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₇₆₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇₆₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇₆₉	C₂×C₇	1	1	yes	characteristic, direct product factor, Sylow
4	C₂×C₇	C₇₆₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇	C₂×C₇₆₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	C₇×C₇₆₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×C₇₆₉	C₂	direct (N × H)
2. C₂×C₇₆₉	C₇	direct (N × H)
3. C₇₆₉	C₂×C₇	direct (N × H)
4. C₂×C₇	C₇₆₉	direct (N × H)
5. C₇	C₂×C₇₆₉	direct (N × H)
6. C₂	C₇×C₇₆₉	direct (N × H)