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Extensions 1→N→G→Q→1 with N=C3 and Q=C6×C7⋊C3

Direct product G=N×Q with N=C3 and Q=C6×C7⋊C3
dρLabelID
C3×C6×C7⋊C3126C3xC6xC7:C3378,52

Semidirect products G=N:Q with N=C3 and Q=C6×C7⋊C3
extensionφ:Q→Aut NdρLabelID
C3⋊(C6×C7⋊C3) = C3×S3×C7⋊C3φ: C6×C7⋊C3/C3×C7⋊C3 → C2 ⊆ Aut C3426C3:(C6xC7:C3)378,48

Non-split extensions G=N.Q with N=C3 and Q=C6×C7⋊C3
extensionφ:Q→Aut NdρLabelID
C3.1(C6×C7⋊C3) = C18×C7⋊C3central extension (φ=1)1263C3.1(C6xC7:C3)378,23
C3.2(C6×C7⋊C3) = C6×C7⋊C9central extension (φ=1)378C3.2(C6xC7:C3)378,26
C3.3(C6×C7⋊C3) = C2×C63⋊C3central stem extension (φ=1)1263C3.3(C6xC7:C3)378,24
C3.4(C6×C7⋊C3) = C2×C63⋊3C3central stem extension (φ=1)1263C3.4(C6xC7:C3)378,25
C3.5(C6×C7⋊C3) = C2×C21.C32central stem extension (φ=1)1263C3.5(C6xC7:C3)378,27
C3.6(C6×C7⋊C3) = C2×C7⋊He3central stem extension (φ=1)1263C3.6(C6xC7:C3)378,28

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