# Extensions 1→N→G→Q→1 with N=C3×C21 and Q=S3

Direct product G=N×Q with N=C3×C21 and Q=S3
dρLabelID
S3×C3×C21126S3xC3xC21378,54

Semidirect products G=N:Q with N=C3×C21 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C21)⋊1S3 = He3⋊D7φ: S3/C1S3 ⊆ Aut C3×C21636+(C3xC21):1S3378,38
(C3×C21)⋊2S3 = C32⋊D21φ: S3/C1S3 ⊆ Aut C3×C21636(C3xC21):2S3378,43
(C3×C21)⋊3S3 = C7×C32⋊C6φ: S3/C1S3 ⊆ Aut C3×C21636(C3xC21):3S3378,34
(C3×C21)⋊4S3 = C7×He3⋊C2φ: S3/C1S3 ⊆ Aut C3×C21633(C3xC21):4S3378,41
(C3×C21)⋊5S3 = C33⋊D7φ: S3/C3C2 ⊆ Aut C3×C21189(C3xC21):5S3378,59
(C3×C21)⋊6S3 = C3×C3⋊D21φ: S3/C3C2 ⊆ Aut C3×C21126(C3xC21):6S3378,57
(C3×C21)⋊7S3 = C32×D21φ: S3/C3C2 ⊆ Aut C3×C21126(C3xC21):7S3378,55
(C3×C21)⋊8S3 = C3⋊S3×C21φ: S3/C3C2 ⊆ Aut C3×C21126(C3xC21):8S3378,56
(C3×C21)⋊9S3 = C7×C33⋊C2φ: S3/C3C2 ⊆ Aut C3×C21189(C3xC21):9S3378,58

Non-split extensions G=N.Q with N=C3×C21 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C21).1S3 = D63⋊C3φ: S3/C1S3 ⊆ Aut C3×C21636+(C3xC21).1S3378,39
(C3×C21).2S3 = C7×C9⋊C6φ: S3/C1S3 ⊆ Aut C3×C21636(C3xC21).2S3378,35
(C3×C21).3S3 = C3⋊D63φ: S3/C3C2 ⊆ Aut C3×C21189(C3xC21).3S3378,42
(C3×C21).4S3 = C3×D63φ: S3/C3C2 ⊆ Aut C3×C211262(C3xC21).4S3378,36
(C3×C21).5S3 = D9×C21φ: S3/C3C2 ⊆ Aut C3×C211262(C3xC21).5S3378,32
(C3×C21).6S3 = C7×C9⋊S3φ: S3/C3C2 ⊆ Aut C3×C21189(C3xC21).6S3378,40

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