# Extensions 1→N→G→Q→1 with N=D4 and Q=C22×C4

Direct product G=N×Q with N=D4 and Q=C22×C4
dρLabelID
D4×C22×C464D4xC2^2xC4128,2154

Semidirect products G=N:Q with N=D4 and Q=C22×C4
extensionφ:Q→Out NdρLabelID
D41(C22×C4) = C2×C4×D8φ: C22×C4/C2×C4C2 ⊆ Out D464D4:1(C2^2xC4)128,1668
D42(C22×C4) = C2×D8⋊C4φ: C22×C4/C2×C4C2 ⊆ Out D464D4:2(C2^2xC4)128,1674
D43(C22×C4) = C4×C8⋊C22φ: C22×C4/C2×C4C2 ⊆ Out D432D4:3(C2^2xC4)128,1676
D44(C22×C4) = C22×D4⋊C4φ: C22×C4/C23C2 ⊆ Out D464D4:4(C2^2xC4)128,1622
D45(C22×C4) = C2×C23.36D4φ: C22×C4/C23C2 ⊆ Out D464D4:5(C2^2xC4)128,1627
D46(C22×C4) = C22×C4≀C2φ: C22×C4/C23C2 ⊆ Out D432D4:6(C2^2xC4)128,1631
D47(C22×C4) = C2×C4×C4○D4φ: trivial image64D4:7(C2^2xC4)128,2156
D48(C22×C4) = C2×C22.11C24φ: trivial image32D4:8(C2^2xC4)128,2157
D49(C22×C4) = C2×C23.33C23φ: trivial image64D4:9(C2^2xC4)128,2159
D410(C22×C4) = C4×2+ 1+4φ: trivial image32D4:10(C2^2xC4)128,2161

Non-split extensions G=N.Q with N=D4 and Q=C22×C4
extensionφ:Q→Out NdρLabelID
D4.1(C22×C4) = C2×C4×SD16φ: C22×C4/C2×C4C2 ⊆ Out D464D4.1(C2^2xC4)128,1669
D4.2(C22×C4) = C4×C4○D8φ: C22×C4/C2×C4C2 ⊆ Out D464D4.2(C2^2xC4)128,1671
D4.3(C22×C4) = C2×SD16⋊C4φ: C22×C4/C2×C4C2 ⊆ Out D464D4.3(C2^2xC4)128,1672
D4.4(C22×C4) = C42.383D4φ: C22×C4/C2×C4C2 ⊆ Out D464D4.4(C2^2xC4)128,1675
D4.5(C22×C4) = C4×C8.C22φ: C22×C4/C2×C4C2 ⊆ Out D464D4.5(C2^2xC4)128,1677
D4.6(C22×C4) = C42.275C23φ: C22×C4/C2×C4C2 ⊆ Out D432D4.6(C2^2xC4)128,1678
D4.7(C22×C4) = C42.276C23φ: C22×C4/C2×C4C2 ⊆ Out D464D4.7(C2^2xC4)128,1679
D4.8(C22×C4) = C42.277C23φ: C22×C4/C2×C4C2 ⊆ Out D432D4.8(C2^2xC4)128,1680
D4.9(C22×C4) = C42.278C23φ: C22×C4/C2×C4C2 ⊆ Out D432D4.9(C2^2xC4)128,1681
D4.10(C22×C4) = C42.280C23φ: C22×C4/C2×C4C2 ⊆ Out D464D4.10(C2^2xC4)128,1683
D4.11(C22×C4) = C42.281C23φ: C22×C4/C2×C4C2 ⊆ Out D464D4.11(C2^2xC4)128,1684
D4.12(C22×C4) = C2×C8○D8φ: C22×C4/C2×C4C2 ⊆ Out D432D4.12(C2^2xC4)128,1685
D4.13(C22×C4) = C2×C8.26D4φ: C22×C4/C2×C4C2 ⊆ Out D432D4.13(C2^2xC4)128,1686
D4.14(C22×C4) = C42.283C23φ: C22×C4/C2×C4C2 ⊆ Out D4324D4.14(C2^2xC4)128,1687
D4.15(C22×C4) = M4(2).51D4φ: C22×C4/C2×C4C2 ⊆ Out D4164D4.15(C2^2xC4)128,1688
D4.16(C22×C4) = M4(2)○D8φ: C22×C4/C2×C4C2 ⊆ Out D4324D4.16(C2^2xC4)128,1689
D4.17(C22×C4) = C2×C23.24D4φ: C22×C4/C23C2 ⊆ Out D464D4.17(C2^2xC4)128,1624
D4.18(C22×C4) = C2×C23.37D4φ: C22×C4/C23C2 ⊆ Out D432D4.18(C2^2xC4)128,1625
D4.19(C22×C4) = C24.98D4φ: C22×C4/C23C2 ⊆ Out D432D4.19(C2^2xC4)128,1628
D4.20(C22×C4) = 2+ 1+45C4φ: C22×C4/C23C2 ⊆ Out D432D4.20(C2^2xC4)128,1629
D4.21(C22×C4) = 2- 1+44C4φ: C22×C4/C23C2 ⊆ Out D464D4.21(C2^2xC4)128,1630
D4.22(C22×C4) = C2×C42⋊C22φ: C22×C4/C23C2 ⊆ Out D432D4.22(C2^2xC4)128,1632
D4.23(C22×C4) = 2- 1+45C4φ: C22×C4/C23C2 ⊆ Out D4164D4.23(C2^2xC4)128,1633
D4.24(C22×C4) = C22.14C25φ: trivial image32D4.24(C2^2xC4)128,2160
D4.25(C22×C4) = C4×2- 1+4φ: trivial image64D4.25(C2^2xC4)128,2162
D4.26(C22×C4) = C22×C8○D4φ: trivial image64D4.26(C2^2xC4)128,2303
D4.27(C22×C4) = C2×Q8○M4(2)φ: trivial image32D4.27(C2^2xC4)128,2304
D4.28(C22×C4) = C4.22C25φ: trivial image324D4.28(C2^2xC4)128,2305

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