# Extensions 1→N→G→Q→1 with N=C6 and Q=C3×M4(2)

Direct product G=N×Q with N=C6 and Q=C3×M4(2)
dρLabelID
M4(2)×C3×C6144M4(2)xC3xC6288,827

Semidirect products G=N:Q with N=C6 and Q=C3×M4(2)
extensionφ:Q→Aut NdρLabelID
C61(C3×M4(2)) = C6×C8⋊S3φ: C3×M4(2)/C24C2 ⊆ Aut C696C6:1(C3xM4(2))288,671
C62(C3×M4(2)) = C6×C4.Dic3φ: C3×M4(2)/C2×C12C2 ⊆ Aut C648C6:2(C3xM4(2))288,692

Non-split extensions G=N.Q with N=C6 and Q=C3×M4(2)
extensionφ:Q→Aut NdρLabelID
C6.1(C3×M4(2)) = C3×Dic3⋊C8φ: C3×M4(2)/C24C2 ⊆ Aut C696C6.1(C3xM4(2))288,248
C6.2(C3×M4(2)) = C3×C24⋊C4φ: C3×M4(2)/C24C2 ⊆ Aut C696C6.2(C3xM4(2))288,249
C6.3(C3×M4(2)) = C3×D6⋊C8φ: C3×M4(2)/C24C2 ⊆ Aut C696C6.3(C3xM4(2))288,254
C6.4(C3×M4(2)) = C3×C42.S3φ: C3×M4(2)/C2×C12C2 ⊆ Aut C696C6.4(C3xM4(2))288,237
C6.5(C3×M4(2)) = C3×C12⋊C8φ: C3×M4(2)/C2×C12C2 ⊆ Aut C696C6.5(C3xM4(2))288,238
C6.6(C3×M4(2)) = C3×C12.55D4φ: C3×M4(2)/C2×C12C2 ⊆ Aut C648C6.6(C3xM4(2))288,264
C6.7(C3×M4(2)) = C9×C8⋊C4central extension (φ=1)288C6.7(C3xM4(2))288,47
C6.8(C3×M4(2)) = C9×C22⋊C8central extension (φ=1)144C6.8(C3xM4(2))288,48
C6.9(C3×M4(2)) = C9×C4⋊C8central extension (φ=1)288C6.9(C3xM4(2))288,55
C6.10(C3×M4(2)) = M4(2)×C18central extension (φ=1)144C6.10(C3xM4(2))288,180
C6.11(C3×M4(2)) = C32×C8⋊C4central extension (φ=1)288C6.11(C3xM4(2))288,315
C6.12(C3×M4(2)) = C32×C22⋊C8central extension (φ=1)144C6.12(C3xM4(2))288,316
C6.13(C3×M4(2)) = C32×C4⋊C8central extension (φ=1)288C6.13(C3xM4(2))288,323

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