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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C7⋊C8

Direct product G=N×Q with N=C2×C4 and Q=C7⋊C8
dρLabelID
C2×C4×C7⋊C8448C2xC4xC7:C8448,454

Semidirect products G=N:Q with N=C2×C4 and Q=C7⋊C8
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊(C7⋊C8) = (C2×C28)⋊C8φ: C7⋊C8/C14 → C4 ⊆ Aut C2×C4224(C2xC4):(C7:C8)448,85
(C2×C4)⋊2(C7⋊C8) = (C2×C28)⋊3C8φ: C7⋊C8/C28 → C2 ⊆ Aut C2×C4448(C2xC4):2(C7:C8)448,81
(C2×C4)⋊3(C7⋊C8) = C2×C28⋊C8φ: C7⋊C8/C28 → C2 ⊆ Aut C2×C4448(C2xC4):3(C7:C8)448,457
(C2×C4)⋊4(C7⋊C8) = C42.6Dic7φ: C7⋊C8/C28 → C2 ⊆ Aut C2×C4224(C2xC4):4(C7:C8)448,459

Non-split extensions G=N.Q with N=C2×C4 and Q=C7⋊C8
extensionφ:Q→Aut NdρLabelID
(C2×C4).(C7⋊C8) = C56.D4φ: C7⋊C8/C14 → C4 ⊆ Aut C2×C41124(C2xC4).(C7:C8)448,110
(C2×C4).2(C7⋊C8) = C56.C8φ: C7⋊C8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).2(C7:C8)448,18
(C2×C4).3(C7⋊C8) = C28⋊C16φ: C7⋊C8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).3(C7:C8)448,19
(C2×C4).4(C7⋊C8) = C56.91D4φ: C7⋊C8/C28 → C2 ⊆ Aut C2×C4224(C2xC4).4(C7:C8)448,106
(C2×C4).5(C7⋊C8) = C7⋊M6(2)φ: C7⋊C8/C28 → C2 ⊆ Aut C2×C42242(C2xC4).5(C7:C8)448,56
(C2×C4).6(C7⋊C8) = C2×C28.C8φ: C7⋊C8/C28 → C2 ⊆ Aut C2×C4224(C2xC4).6(C7:C8)448,631
(C2×C4).7(C7⋊C8) = C4×C7⋊C16central extension (φ=1)448(C2xC4).7(C7:C8)448,17
(C2×C4).8(C7⋊C8) = C2×C7⋊C32central extension (φ=1)448(C2xC4).8(C7:C8)448,55
(C2×C4).9(C7⋊C8) = C22×C7⋊C16central extension (φ=1)448(C2xC4).9(C7:C8)448,630

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