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

Direct product G=N×Q with N=C4 and Q=C8⋊C4
dρLabelID
C4×C8⋊C4128C4xC8:C4128,457

Semidirect products G=N:Q with N=C4 and Q=C8⋊C4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C8⋊C4) = C43.7C2φ: C8⋊C4/C42 → C2 ⊆ Aut C4128C4:1(C8:C4)128,499
C4⋊2(C8⋊C4) = C4⋊C8⋊13C4φ: C8⋊C4/C2×C8 → C2 ⊆ Aut C4128C4:2(C8:C4)128,502

Non-split extensions G=N.Q with N=C4 and Q=C8⋊C4
extensionφ:Q→Aut NdρLabelID
C4.1(C8⋊C4) = C42⋊6C8φ: C8⋊C4/C42 → C2 ⊆ Aut C432C4.1(C8:C4)128,8
C4.2(C8⋊C4) = C42.385D4φ: C8⋊C4/C42 → C2 ⊆ Aut C4128C4.2(C8:C4)128,9
C4.3(C8⋊C4) = M5(2)⋊C4φ: C8⋊C4/C42 → C2 ⊆ Aut C464C4.3(C8:C4)128,109
C4.4(C8⋊C4) = C23.27C42φ: C8⋊C4/C42 → C2 ⊆ Aut C464C4.4(C8:C4)128,184
C4.5(C8⋊C4) = C2×C16⋊C4φ: C8⋊C4/C42 → C2 ⊆ Aut C432C4.5(C8:C4)128,841
C4.6(C8⋊C4) = M4(2)⋊C8φ: C8⋊C4/C2×C8 → C2 ⊆ Aut C464C4.6(C8:C4)128,10
C4.7(C8⋊C4) = C42.46Q8φ: C8⋊C4/C2×C8 → C2 ⊆ Aut C4128C4.7(C8:C4)128,11
C4.8(C8⋊C4) = M4(2).C8φ: C8⋊C4/C2×C8 → C2 ⊆ Aut C4324C4.8(C8:C4)128,110
C4.9(C8⋊C4) = C8⋊9M4(2)φ: C8⋊C4/C2×C8 → C2 ⊆ Aut C464C4.9(C8:C4)128,183
C4.10(C8⋊C4) = C8.23C42φ: C8⋊C4/C2×C8 → C2 ⊆ Aut C4324C4.10(C8:C4)128,842
C4.11(C8⋊C4) = C42⋊1C8central extension (φ=1)32C4.11(C8:C4)128,6
C4.12(C8⋊C4) = C42.20D4central extension (φ=1)64C4.12(C8:C4)128,7
C4.13(C8⋊C4) = C8⋊C16central extension (φ=1)128C4.13(C8:C4)128,44
C4.14(C8⋊C4) = C16⋊C8central extension (φ=1)128C4.14(C8:C4)128,45
C4.15(C8⋊C4) = C22.7M5(2)central extension (φ=1)128C4.15(C8:C4)128,106
C4.16(C8⋊C4) = C2×C8⋊C8central extension (φ=1)128C4.16(C8:C4)128,180
C4.17(C8⋊C4) = C42⋊4C8central extension (φ=1)128C4.17(C8:C4)128,476

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