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Extensions 1→N→G→Q→1 with N=C2×C34 and Q=S3

Direct product G=N×Q with N=C2×C34 and Q=S3
dρLabelID
S3×C2×C34204S3xC2xC34408,44

Semidirect products G=N:Q with N=C2×C34 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C34)⋊1S3 = C17×S4φ: S3/C1 → S3 ⊆ Aut C2×C34683(C2xC34):1S3408,36
(C2×C34)⋊2S3 = C17⋊S4φ: S3/C1 → S3 ⊆ Aut C2×C34686+(C2xC34):2S3408,37
(C2×C34)⋊3S3 = C17×C3⋊D4φ: S3/C3 → C2 ⊆ Aut C2×C342042(C2xC34):3S3408,24
(C2×C34)⋊4S3 = C51⋊7D4φ: S3/C3 → C2 ⊆ Aut C2×C342042(C2xC34):4S3408,29
(C2×C34)⋊5S3 = C22×D51φ: S3/C3 → C2 ⊆ Aut C2×C34204(C2xC34):5S3408,45

Non-split extensions G=N.Q with N=C2×C34 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C34).S3 = C2×Dic51φ: S3/C3 → C2 ⊆ Aut C2×C34408(C2xC34).S3408,28
(C2×C34).2S3 = Dic3×C34central extension (φ=1)408(C2xC34).2S3408,23

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