# Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C2×C7⋊C3

Direct product G=N×Q with N=C2×C4 and Q=C2×C7⋊C3
dρLabelID
C22×C4×C7⋊C3112C2^2xC4xC7:C3336,164

Semidirect products G=N:Q with N=C2×C4 and Q=C2×C7⋊C3
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×C7⋊C3) = C22⋊C4×C7⋊C3φ: C2×C7⋊C3/C7⋊C3C2 ⊆ Aut C2×C456(C2xC4):1(C2xC7:C3)336,49
(C2×C4)⋊2(C2×C7⋊C3) = C2×D4×C7⋊C3φ: C2×C7⋊C3/C7⋊C3C2 ⊆ Aut C2×C456(C2xC4):2(C2xC7:C3)336,165
(C2×C4)⋊3(C2×C7⋊C3) = C4○D4×C7⋊C3φ: C2×C7⋊C3/C7⋊C3C2 ⊆ Aut C2×C4566(C2xC4):3(C2xC7:C3)336,167

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×C7⋊C3
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×C7⋊C3) = C4⋊C4×C7⋊C3φ: C2×C7⋊C3/C7⋊C3C2 ⊆ Aut C2×C4112(C2xC4).1(C2xC7:C3)336,50
(C2×C4).2(C2×C7⋊C3) = M4(2)×C7⋊C3φ: C2×C7⋊C3/C7⋊C3C2 ⊆ Aut C2×C4566(C2xC4).2(C2xC7:C3)336,52
(C2×C4).3(C2×C7⋊C3) = C2×Q8×C7⋊C3φ: C2×C7⋊C3/C7⋊C3C2 ⊆ Aut C2×C4112(C2xC4).3(C2xC7:C3)336,166
(C2×C4).4(C2×C7⋊C3) = C42×C7⋊C3central extension (φ=1)112(C2xC4).4(C2xC7:C3)336,48
(C2×C4).5(C2×C7⋊C3) = C2×C8×C7⋊C3central extension (φ=1)112(C2xC4).5(C2xC7:C3)336,51

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