# Extensions 1→N→G→Q→1 with N=C14 and Q=C2×C6

Direct product G=N×Q with N=C14 and Q=C2×C6
dρLabelID
C22×C42168C2^2xC42168,57

Semidirect products G=N:Q with N=C14 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C14⋊(C2×C6) = C22×F7φ: C2×C6/C2C6 ⊆ Aut C1428C14:(C2xC6)168,47
C142(C2×C6) = C23×C7⋊C3φ: C2×C6/C22C3 ⊆ Aut C1456C14:2(C2xC6)168,51
C143(C2×C6) = C2×C6×D7φ: C2×C6/C6C2 ⊆ Aut C1484C14:3(C2xC6)168,54

Non-split extensions G=N.Q with N=C14 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C14.1(C2×C6) = C4.F7φ: C2×C6/C2C6 ⊆ Aut C14566-C14.1(C2xC6)168,7
C14.2(C2×C6) = C4×F7φ: C2×C6/C2C6 ⊆ Aut C14286C14.2(C2xC6)168,8
C14.3(C2×C6) = C4⋊F7φ: C2×C6/C2C6 ⊆ Aut C14286+C14.3(C2xC6)168,9
C14.4(C2×C6) = C2×C7⋊C12φ: C2×C6/C2C6 ⊆ Aut C1456C14.4(C2xC6)168,10
C14.5(C2×C6) = Dic7⋊C6φ: C2×C6/C2C6 ⊆ Aut C14286C14.5(C2xC6)168,11
C14.6(C2×C6) = C2×C4×C7⋊C3φ: C2×C6/C22C3 ⊆ Aut C1456C14.6(C2xC6)168,19
C14.7(C2×C6) = D4×C7⋊C3φ: C2×C6/C22C3 ⊆ Aut C14286C14.7(C2xC6)168,20
C14.8(C2×C6) = Q8×C7⋊C3φ: C2×C6/C22C3 ⊆ Aut C14566C14.8(C2xC6)168,21
C14.9(C2×C6) = C3×Dic14φ: C2×C6/C6C2 ⊆ Aut C141682C14.9(C2xC6)168,24
C14.10(C2×C6) = C12×D7φ: C2×C6/C6C2 ⊆ Aut C14842C14.10(C2xC6)168,25
C14.11(C2×C6) = C3×D28φ: C2×C6/C6C2 ⊆ Aut C14842C14.11(C2xC6)168,26
C14.12(C2×C6) = C6×Dic7φ: C2×C6/C6C2 ⊆ Aut C14168C14.12(C2xC6)168,27
C14.13(C2×C6) = C3×C7⋊D4φ: C2×C6/C6C2 ⊆ Aut C14842C14.13(C2xC6)168,28
C14.14(C2×C6) = D4×C21central extension (φ=1)842C14.14(C2xC6)168,40
C14.15(C2×C6) = Q8×C21central extension (φ=1)1682C14.15(C2xC6)168,41

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