Finite Group Databasebeta

← C₃×C₇×C₃₃₁ #20294331

Subgroups — C₃×C₇×C₃₃₁ #20294331

Order 6951.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₃₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₃₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
4	C₃×C₇	C₃₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇	C₃×C₃₃₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	C₇×C₃₃₁	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×C₃₃₁	C₃	direct (N × H)
2. C₃×C₃₃₁	C₇	direct (N × H)
3. C₃₃₁	C₃×C₇	direct (N × H)
4. C₃×C₇	C₃₃₁	direct (N × H)
5. C₇	C₃×C₃₃₁	direct (N × H)
6. C₃	C₇×C₃₃₁	direct (N × H)