# Extensions 1→N→G→Q→1 with N=C14 and Q=C2×A4

Direct product G=N×Q with N=C14 and Q=C2×A4
dρLabelID
A4×C2×C1484A4xC2xC14336,221

Semidirect products G=N:Q with N=C14 and Q=C2×A4
extensionφ:Q→Aut NdρLabelID
C14⋊(C2×A4) = C2×D7⋊A4φ: C2×A4/C22C6 ⊆ Aut C14426+C14:(C2xA4)336,218
C142(C2×A4) = C22×C7⋊A4φ: C2×A4/C23C3 ⊆ Aut C1484C14:2(C2xA4)336,222
C143(C2×A4) = C2×A4×D7φ: C2×A4/A4C2 ⊆ Aut C14426+C14:3(C2xA4)336,217

Non-split extensions G=N.Q with N=C14 and Q=C2×A4
extensionφ:Q→Aut NdρLabelID
C14.1(C2×A4) = Q8.F7φ: C2×A4/C22C6 ⊆ Aut C1411212+C14.1(C2xA4)336,134
C14.2(C2×A4) = Q8⋊F7φ: C2×A4/C22C6 ⊆ Aut C145612-C14.2(C2xA4)336,135
C14.3(C2×A4) = Dic7⋊A4φ: C2×A4/C22C6 ⊆ Aut C14846-C14.3(C2xA4)336,136
C14.4(C2×A4) = C4×C7⋊A4φ: C2×A4/C23C3 ⊆ Aut C14843C14.4(C2xA4)336,171
C14.5(C2×A4) = C2×C14.A4φ: C2×A4/C23C3 ⊆ Aut C14112C14.5(C2xA4)336,172
C14.6(C2×A4) = C28.A4φ: C2×A4/C23C3 ⊆ Aut C141126C14.6(C2xA4)336,173
C14.7(C2×A4) = Dic7.2A4φ: C2×A4/A4C2 ⊆ Aut C141124+C14.7(C2xA4)336,131
C14.8(C2×A4) = D7×SL2(𝔽3)φ: C2×A4/A4C2 ⊆ Aut C14564-C14.8(C2xA4)336,132
C14.9(C2×A4) = A4×Dic7φ: C2×A4/A4C2 ⊆ Aut C14846-C14.9(C2xA4)336,133
C14.10(C2×A4) = A4×C28central extension (φ=1)843C14.10(C2xA4)336,168
C14.11(C2×A4) = C14×SL2(𝔽3)central extension (φ=1)112C14.11(C2xA4)336,169
C14.12(C2×A4) = C7×C4.A4central extension (φ=1)1122C14.12(C2xA4)336,170

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