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The query <q>[[Satisfies property::Normal subgroup]] [[Dissatisfies property::Direct factor]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Dissatisfies property.Weaker than::Direct factor]] [[Category:Particular subgroups]]</q> was answered by the SMWSQLStore3 in 0.0215 seconds.

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 Group partSubgroup partQuotient part
A3 in S3Symmetric group:S3Cyclic group:Z3Cyclic group:Z2
A4 in S4Symmetric group:S4Alternating group:A4Cyclic group:Z2
Center of M16M16Cyclic group:Z4Klein four-group
Center of dihedral group:D8Dihedral group:D8Cyclic group:Z2Klein four-group
Center of unitriangular matrix group:UT(3,p)Unitriangular matrix group:UT(3,p)Group of prime orderElementary abelian group of prime-square order
Cyclic maximal subgroup of dihedral group:D16Dihedral group:D16Cyclic group:Z8Cyclic group:Z2
Cyclic maximal subgroup of dihedral group:D8Dihedral group:D8Cyclic group:Z4Cyclic group:Z2
Cyclic maximal subgroup of semidihedral group:SD16Semidihedral group:SD16Cyclic group:Z8Cyclic group:Z2
Derived subgroup of M16M16Cyclic group:Z2Direct product of Z4 and Z2
Derived subgroup of nontrivial semidirect product of Z4 and Z4Nontrivial semidirect product of Z4 and Z4Cyclic group:Z2Direct product of Z4 and Z2
Direct product of Z4 and Z2 in M16M16Direct product of Z4 and Z2Cyclic group:Z2
Klein four-subgroup of M16M16Klein four-groupCyclic group:Z4
Klein four-subgroup of alternating group:A4Alternating group:A4Klein four-groupCyclic group:Z3
Klein four-subgroups of dihedral group:D8Dihedral group:D8Klein four-groupCyclic group:Z2
Normal Klein four-subgroup of symmetric group:S4Symmetric group:S4Klein four-groupSymmetric group:S3
SL(2,3) in GL(2,3)General linear group:GL(2,3)Special linear group:SL(2,3)Cyclic group:Z2
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