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Extensions 1→N→G→Q→1 with N=C4 and Q=C56⋊C2

Direct product G=N×Q with N=C4 and Q=C56⋊C2
dρLabelID
C4×C56⋊C2224C4xC56:C2448,225

Semidirect products G=N:Q with N=C4 and Q=C56⋊C2
extensionφ:Q→Aut NdρLabelID
C4⋊1(C56⋊C2) = C8⋊5D28φ: C56⋊C2/C56 → C2 ⊆ Aut C4224C4:1(C56:C2)448,227
C4⋊2(C56⋊C2) = Dic14⋊8D4φ: C56⋊C2/Dic14 → C2 ⊆ Aut C4224C4:2(C56:C2)448,382
C4⋊3(C56⋊C2) = C28⋊SD16φ: C56⋊C2/D28 → C2 ⊆ Aut C4224C4:3(C56:C2)448,375

Non-split extensions G=N.Q with N=C4 and Q=C56⋊C2
extensionφ:Q→Aut NdρLabelID
C4.1(C56⋊C2) = C56.78D4φ: C56⋊C2/C56 → C2 ⊆ Aut C4448C4.1(C56:C2)448,60
C4.2(C56⋊C2) = C2.D112φ: C56⋊C2/C56 → C2 ⊆ Aut C4224C4.2(C56:C2)448,66
C4.3(C56⋊C2) = C56⋊9Q8φ: C56⋊C2/C56 → C2 ⊆ Aut C4448C4.3(C56:C2)448,214
C4.4(C56⋊C2) = C28.14Q16φ: C56⋊C2/C56 → C2 ⊆ Aut C4448C4.4(C56:C2)448,215
C4.5(C56⋊C2) = C4.5D56φ: C56⋊C2/C56 → C2 ⊆ Aut C4224C4.5(C56:C2)448,228
C4.6(C56⋊C2) = C4.D56φ: C56⋊C2/Dic14 → C2 ⊆ Aut C4224C4.6(C56:C2)448,42
C4.7(C56⋊C2) = C28.2D8φ: C56⋊C2/Dic14 → C2 ⊆ Aut C4448C4.7(C56:C2)448,43
C4.8(C56⋊C2) = Dic14⋊4Q8φ: C56⋊C2/Dic14 → C2 ⊆ Aut C4448C4.8(C56:C2)448,385
C4.9(C56⋊C2) = C4.Dic28φ: C56⋊C2/D28 → C2 ⊆ Aut C4448C4.9(C56:C2)448,38
C4.10(C56⋊C2) = C28.47D8φ: C56⋊C2/D28 → C2 ⊆ Aut C4448C4.10(C56:C2)448,39
C4.11(C56⋊C2) = C16⋊Dic7φ: C56⋊C2/D28 → C2 ⊆ Aut C41124C4.11(C56:C2)448,70
C4.12(C56⋊C2) = D56⋊2C4φ: C56⋊C2/D28 → C2 ⊆ Aut C41124C4.12(C56:C2)448,75
C4.13(C56⋊C2) = D28⋊3Q8φ: C56⋊C2/D28 → C2 ⊆ Aut C4224C4.13(C56:C2)448,376
C4.14(C56⋊C2) = C4.8Dic28central extension (φ=1)448C4.14(C56:C2)448,13
C4.15(C56⋊C2) = C56⋊2C8central extension (φ=1)448C4.15(C56:C2)448,14
C4.16(C56⋊C2) = C4.17D56central extension (φ=1)224C4.16(C56:C2)448,16

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