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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C7×Q8

Direct product G=N×Q with N=C2×C4 and Q=C7×Q8
dρLabelID
Q8×C2×C28448Q8xC2xC28448,1299

Semidirect products G=N:Q with N=C2×C4 and Q=C7×Q8
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C7×Q8) = C7×C23.78C23φ: C7×Q8/C14 → C22 ⊆ Aut C2×C4448(C2xC4):1(C7xQ8)448,803
(C2×C4)⋊2(C7×Q8) = C7×C23.41C23φ: C7×Q8/C14 → C22 ⊆ Aut C2×C4224(C2xC4):2(C7xQ8)448,1327
(C2×C4)⋊3(C7×Q8) = C7×C23.67C23φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4):3(C7xQ8)448,799
(C2×C4)⋊4(C7×Q8) = C14×C4⋊Q8φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4):4(C7xQ8)448,1314
(C2×C4)⋊5(C7×Q8) = C7×C23.37C23φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4224(C2xC4):5(C7xQ8)448,1316

Non-split extensions G=N.Q with N=C2×C4 and Q=C7×Q8
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C7×Q8) = C7×C4.9C42φ: C7×Q8/C14 → C22 ⊆ Aut C2×C41124(C2xC4).1(C7xQ8)448,141
(C2×C4).2(C7×Q8) = C7×C22.C42φ: C7×Q8/C14 → C22 ⊆ Aut C2×C4224(C2xC4).2(C7xQ8)448,147
(C2×C4).3(C7×Q8) = C7×M4(2)⋊4C4φ: C7×Q8/C14 → C22 ⊆ Aut C2×C41124(C2xC4).3(C7xQ8)448,148
(C2×C4).4(C7×Q8) = C7×C23.81C23φ: C7×Q8/C14 → C22 ⊆ Aut C2×C4448(C2xC4).4(C7xQ8)448,806
(C2×C4).5(C7×Q8) = C7×C23.83C23φ: C7×Q8/C14 → C22 ⊆ Aut C2×C4448(C2xC4).5(C7xQ8)448,808
(C2×C4).6(C7×Q8) = C7×M4(2)⋊C4φ: C7×Q8/C14 → C22 ⊆ Aut C2×C4224(C2xC4).6(C7xQ8)448,836
(C2×C4).7(C7×Q8) = C7×M4(2).C4φ: C7×Q8/C14 → C22 ⊆ Aut C2×C41124(C2xC4).7(C7xQ8)448,838
(C2×C4).8(C7×Q8) = C7×C8⋊2C8φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).8(C7xQ8)448,138
(C2×C4).9(C7×Q8) = C7×C8⋊1C8φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).9(C7xQ8)448,139
(C2×C4).10(C7×Q8) = C7×C23.63C23φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).10(C7xQ8)448,795
(C2×C4).11(C7×Q8) = C7×C23.65C23φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).11(C7xQ8)448,797
(C2×C4).12(C7×Q8) = C7×C42⋊6C4φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4112(C2xC4).12(C7xQ8)448,143
(C2×C4).13(C7×Q8) = C7×C22.4Q16φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).13(C7xQ8)448,144
(C2×C4).14(C7×Q8) = C7×C42⋊8C4φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).14(C7xQ8)448,790
(C2×C4).15(C7×Q8) = C7×C42⋊9C4φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).15(C7xQ8)448,792
(C2×C4).16(C7×Q8) = C7×C4⋊M4(2)φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4224(C2xC4).16(C7xQ8)448,831
(C2×C4).17(C7×Q8) = C7×C42.6C22φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4224(C2xC4).17(C7xQ8)448,832
(C2×C4).18(C7×Q8) = C14×C4.Q8φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).18(C7xQ8)448,833
(C2×C4).19(C7×Q8) = C14×C2.D8φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).19(C7xQ8)448,834
(C2×C4).20(C7×Q8) = C7×C23.25D4φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4224(C2xC4).20(C7xQ8)448,835
(C2×C4).21(C7×Q8) = C14×C8.C4φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4224(C2xC4).21(C7xQ8)448,837
(C2×C4).22(C7×Q8) = C14×C42.C2φ: C7×Q8/C28 → C2 ⊆ Aut C2×C4448(C2xC4).22(C7xQ8)448,1310
(C2×C4).23(C7×Q8) = C7×C22.7C42central extension (φ=1)448(C2xC4).23(C7xQ8)448,140
(C2×C4).24(C7×Q8) = C4⋊C4×C28central extension (φ=1)448(C2xC4).24(C7xQ8)448,786
(C2×C4).25(C7×Q8) = C14×C4⋊C8central extension (φ=1)448(C2xC4).25(C7xQ8)448,830

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