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

Direct product G=N×Q with N=C4 and Q=C4⋊C4
dρLabelID
C4×C4⋊C464C4xC4:C464,59

Semidirect products G=N:Q with N=C4 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C41(C4⋊C4) = C429C4φ: C4⋊C4/C2×C4C2 ⊆ Aut C464C4:1(C4:C4)64,65
C42(C4⋊C4) = C23.65C23φ: C4⋊C4/C2×C4C2 ⊆ Aut C464C4:2(C4:C4)64,70

Non-split extensions G=N.Q with N=C4 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C4.1(C4⋊C4) = C4.9C42φ: C4⋊C4/C2×C4C2 ⊆ Aut C4164C4.1(C4:C4)64,18
C4.2(C4⋊C4) = C426C4φ: C4⋊C4/C2×C4C2 ⊆ Aut C416C4.2(C4:C4)64,20
C4.3(C4⋊C4) = C22.4Q16φ: C4⋊C4/C2×C4C2 ⊆ Aut C464C4.3(C4:C4)64,21
C4.4(C4⋊C4) = C22.C42φ: C4⋊C4/C2×C4C2 ⊆ Aut C432C4.4(C4:C4)64,24
C4.5(C4⋊C4) = M4(2)⋊4C4φ: C4⋊C4/C2×C4C2 ⊆ Aut C4164C4.5(C4:C4)64,25
C4.6(C4⋊C4) = C8.Q8φ: C4⋊C4/C2×C4C2 ⊆ Aut C4164C4.6(C4:C4)64,46
C4.7(C4⋊C4) = C163C4φ: C4⋊C4/C2×C4C2 ⊆ Aut C464C4.7(C4:C4)64,47
C4.8(C4⋊C4) = C164C4φ: C4⋊C4/C2×C4C2 ⊆ Aut C464C4.8(C4:C4)64,48
C4.9(C4⋊C4) = C8.4Q8φ: C4⋊C4/C2×C4C2 ⊆ Aut C4322C4.9(C4:C4)64,49
C4.10(C4⋊C4) = C428C4φ: C4⋊C4/C2×C4C2 ⊆ Aut C464C4.10(C4:C4)64,63
C4.11(C4⋊C4) = C4⋊M4(2)φ: C4⋊C4/C2×C4C2 ⊆ Aut C432C4.11(C4:C4)64,104
C4.12(C4⋊C4) = C42.6C22φ: C4⋊C4/C2×C4C2 ⊆ Aut C432C4.12(C4:C4)64,105
C4.13(C4⋊C4) = C2×C4.Q8φ: C4⋊C4/C2×C4C2 ⊆ Aut C464C4.13(C4:C4)64,106
C4.14(C4⋊C4) = C2×C2.D8φ: C4⋊C4/C2×C4C2 ⊆ Aut C464C4.14(C4:C4)64,107
C4.15(C4⋊C4) = M4(2)⋊C4φ: C4⋊C4/C2×C4C2 ⊆ Aut C432C4.15(C4:C4)64,109
C4.16(C4⋊C4) = C2×C8.C4φ: C4⋊C4/C2×C4C2 ⊆ Aut C432C4.16(C4:C4)64,110
C4.17(C4⋊C4) = M4(2).C4φ: C4⋊C4/C2×C4C2 ⊆ Aut C4164C4.17(C4:C4)64,111
C4.18(C4⋊C4) = C22.7C42central extension (φ=1)64C4.18(C4:C4)64,17
C4.19(C4⋊C4) = C4⋊C16central extension (φ=1)64C4.19(C4:C4)64,44
C4.20(C4⋊C4) = C8.C8central extension (φ=1)162C4.20(C4:C4)64,45
C4.21(C4⋊C4) = C2×C4⋊C8central extension (φ=1)64C4.21(C4:C4)64,103
C4.22(C4⋊C4) = C23.25D4central extension (φ=1)32C4.22(C4:C4)64,108

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