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

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

Semidirect products G=N:Q with N=C7×Q8 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C7×Q8)⋊1(C2×C4) = Dic7⋊7SD16φ: C2×C4/C2 → C22 ⊆ Out C7×Q8224(C7xQ8):1(C2xC4)448,322
(C7×Q8)⋊2(C2×C4) = D7×Q8⋊C4φ: C2×C4/C2 → C22 ⊆ Out C7×Q8224(C7xQ8):2(C2xC4)448,335
(C7×Q8)⋊3(C2×C4) = Q8⋊(C4×D7)φ: C2×C4/C2 → C22 ⊆ Out C7×Q8224(C7xQ8):3(C2xC4)448,337
(C7×Q8)⋊4(C2×C4) = Q8⋊D7⋊C4φ: C2×C4/C2 → C22 ⊆ Out C7×Q8224(C7xQ8):4(C2xC4)448,351
(C7×Q8)⋊5(C2×C4) = D7×C4≀C2φ: C2×C4/C2 → C22 ⊆ Out C7×Q8564(C7xQ8):5(C2xC4)448,354
(C7×Q8)⋊6(C2×C4) = SD16×Dic7φ: C2×C4/C2 → C22 ⊆ Out C7×Q8224(C7xQ8):6(C2xC4)448,695
(C7×Q8)⋊7(C2×C4) = SD16⋊Dic7φ: C2×C4/C2 → C22 ⊆ Out C7×Q8224(C7xQ8):7(C2xC4)448,698
(C7×Q8)⋊8(C2×C4) = C4×Q8⋊D7φ: C2×C4/C4 → C2 ⊆ Out C7×Q8224(C7xQ8):8(C2xC4)448,559
(C7×Q8)⋊9(C2×C4) = C42.56D14φ: C2×C4/C4 → C2 ⊆ Out C7×Q8224(C7xQ8):9(C2xC4)448,560
(C7×Q8)⋊10(C2×C4) = C4×Q8×D7φ: C2×C4/C4 → C2 ⊆ Out C7×Q8224(C7xQ8):10(C2xC4)448,1024
(C7×Q8)⋊11(C2×C4) = C4×Q8⋊2D7φ: C2×C4/C4 → C2 ⊆ Out C7×Q8224(C7xQ8):11(C2xC4)448,1026
(C7×Q8)⋊12(C2×C4) = C42.126D14φ: C2×C4/C4 → C2 ⊆ Out C7×Q8224(C7xQ8):12(C2xC4)448,1027
(C7×Q8)⋊13(C2×C4) = SD16×C28φ: C2×C4/C4 → C2 ⊆ Out C7×Q8224(C7xQ8):13(C2xC4)448,846
(C7×Q8)⋊14(C2×C4) = C7×SD16⋊C4φ: C2×C4/C4 → C2 ⊆ Out C7×Q8224(C7xQ8):14(C2xC4)448,848
(C7×Q8)⋊15(C2×C4) = C2×Q8⋊Dic7φ: C2×C4/C22 → C2 ⊆ Out C7×Q8448(C7xQ8):15(C2xC4)448,758
(C7×Q8)⋊16(C2×C4) = C4○D4⋊Dic7φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8):16(C2xC4)448,766
(C7×Q8)⋊17(C2×C4) = C2×D4⋊2Dic7φ: C2×C4/C22 → C2 ⊆ Out C7×Q8112(C7xQ8):17(C2xC4)448,769
(C7×Q8)⋊18(C2×C4) = C2×Q8×Dic7φ: C2×C4/C22 → C2 ⊆ Out C7×Q8448(C7xQ8):18(C2xC4)448,1264
(C7×Q8)⋊19(C2×C4) = C4○D4×Dic7φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8):19(C2xC4)448,1279
(C7×Q8)⋊20(C2×C4) = C14.1062- 1+4φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8):20(C2xC4)448,1280
(C7×Q8)⋊21(C2×C4) = C14×Q8⋊C4φ: C2×C4/C22 → C2 ⊆ Out C7×Q8448(C7xQ8):21(C2xC4)448,823
(C7×Q8)⋊22(C2×C4) = C7×C23.36D4φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8):22(C2xC4)448,825
(C7×Q8)⋊23(C2×C4) = C14×C4≀C2φ: C2×C4/C22 → C2 ⊆ Out C7×Q8112(C7xQ8):23(C2xC4)448,828
(C7×Q8)⋊24(C2×C4) = C4○D4×C28φ: trivial image224(C7xQ8):24(C2xC4)448,1300
(C7×Q8)⋊25(C2×C4) = C7×C23.33C23φ: trivial image224(C7xQ8):25(C2xC4)448,1303

Non-split extensions G=N.Q with N=C7×Q8 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C7×Q8).1(C2×C4) = C7⋊Q16⋊C4φ: C2×C4/C2 → C22 ⊆ Out C7×Q8448(C7xQ8).1(C2xC4)448,323
(C7×Q8).2(C2×C4) = Dic7⋊4Q16φ: C2×C4/C2 → C22 ⊆ Out C7×Q8448(C7xQ8).2(C2xC4)448,324
(C7×Q8).3(C2×C4) = (Q8×D7)⋊C4φ: C2×C4/C2 → C22 ⊆ Out C7×Q8224(C7xQ8).3(C2xC4)448,336
(C7×Q8).4(C2×C4) = Q8⋊2D7⋊C4φ: C2×C4/C2 → C22 ⊆ Out C7×Q8224(C7xQ8).4(C2xC4)448,338
(C7×Q8).5(C2×C4) = C42⋊D14φ: C2×C4/C2 → C22 ⊆ Out C7×Q81124(C7xQ8).5(C2xC4)448,355
(C7×Q8).6(C2×C4) = M4(2).22D14φ: C2×C4/C2 → C22 ⊆ Out C7×Q81124(C7xQ8).6(C2xC4)448,357
(C7×Q8).7(C2×C4) = C42.196D14φ: C2×C4/C2 → C22 ⊆ Out C7×Q81124(C7xQ8).7(C2xC4)448,358
(C7×Q8).8(C2×C4) = Q16×Dic7φ: C2×C4/C2 → C22 ⊆ Out C7×Q8448(C7xQ8).8(C2xC4)448,717
(C7×Q8).9(C2×C4) = Q16⋊Dic7φ: C2×C4/C2 → C22 ⊆ Out C7×Q8448(C7xQ8).9(C2xC4)448,718
(C7×Q8).10(C2×C4) = D8⋊5Dic7φ: C2×C4/C2 → C22 ⊆ Out C7×Q81124(C7xQ8).10(C2xC4)448,730
(C7×Q8).11(C2×C4) = D8⋊4Dic7φ: C2×C4/C2 → C22 ⊆ Out C7×Q81124(C7xQ8).11(C2xC4)448,731
(C7×Q8).12(C2×C4) = C4×C7⋊Q16φ: C2×C4/C4 → C2 ⊆ Out C7×Q8448(C7xQ8).12(C2xC4)448,563
(C7×Q8).13(C2×C4) = C42.59D14φ: C2×C4/C4 → C2 ⊆ Out C7×Q8448(C7xQ8).13(C2xC4)448,564
(C7×Q8).14(C2×C4) = C56.93D4φ: C2×C4/C4 → C2 ⊆ Out C7×Q81124(C7xQ8).14(C2xC4)448,678
(C7×Q8).15(C2×C4) = C56.50D4φ: C2×C4/C4 → C2 ⊆ Out C7×Q81124(C7xQ8).15(C2xC4)448,679
(C7×Q8).16(C2×C4) = C42.125D14φ: C2×C4/C4 → C2 ⊆ Out C7×Q8224(C7xQ8).16(C2xC4)448,1025
(C7×Q8).17(C2×C4) = D7×C8○D4φ: C2×C4/C4 → C2 ⊆ Out C7×Q81124(C7xQ8).17(C2xC4)448,1202
(C7×Q8).18(C2×C4) = C56.49C23φ: C2×C4/C4 → C2 ⊆ Out C7×Q81124(C7xQ8).18(C2xC4)448,1203
(C7×Q8).19(C2×C4) = Q16×C28φ: C2×C4/C4 → C2 ⊆ Out C7×Q8448(C7xQ8).19(C2xC4)448,847
(C7×Q8).20(C2×C4) = C7×Q16⋊C4φ: C2×C4/C4 → C2 ⊆ Out C7×Q8448(C7xQ8).20(C2xC4)448,849
(C7×Q8).21(C2×C4) = C7×C8○D8φ: C2×C4/C4 → C2 ⊆ Out C7×Q81122(C7xQ8).21(C2xC4)448,851
(C7×Q8).22(C2×C4) = C7×C8.26D4φ: C2×C4/C4 → C2 ⊆ Out C7×Q81124(C7xQ8).22(C2xC4)448,852
(C7×Q8).23(C2×C4) = (Q8×C14)⋊6C4φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8).23(C2xC4)448,759
(C7×Q8).24(C2×C4) = C28.(C2×D4)φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8).24(C2xC4)448,767
(C7×Q8).25(C2×C4) = (D4×C14)⋊9C4φ: C2×C4/C22 → C2 ⊆ Out C7×Q81124(C7xQ8).25(C2xC4)448,770
(C7×Q8).26(C2×C4) = C14.422- 1+4φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8).26(C2xC4)448,1265
(C7×Q8).27(C2×C4) = C2×Q8.Dic7φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8).27(C2xC4)448,1271
(C7×Q8).28(C2×C4) = C28.76C24φ: C2×C4/C22 → C2 ⊆ Out C7×Q81124(C7xQ8).28(C2xC4)448,1272
(C7×Q8).29(C2×C4) = C7×C23.24D4φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8).29(C2xC4)448,824
(C7×Q8).30(C2×C4) = C7×C23.38D4φ: C2×C4/C22 → C2 ⊆ Out C7×Q8224(C7xQ8).30(C2xC4)448,827
(C7×Q8).31(C2×C4) = C7×C42⋊C22φ: C2×C4/C22 → C2 ⊆ Out C7×Q81124(C7xQ8).31(C2xC4)448,829
(C7×Q8).32(C2×C4) = C7×C23.32C23φ: trivial image224(C7xQ8).32(C2xC4)448,1302
(C7×Q8).33(C2×C4) = C14×C8○D4φ: trivial image224(C7xQ8).33(C2xC4)448,1350
(C7×Q8).34(C2×C4) = C7×Q8○M4(2)φ: trivial image1124(C7xQ8).34(C2xC4)448,1351

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