# Extensions 1→N→G→Q→1 with N=C7×Q8 and Q=S3

Direct product G=N×Q with N=C7×Q8 and Q=S3
dρLabelID
S3×C7×Q81684S3xC7xQ8336,190

Semidirect products G=N:Q with N=C7×Q8 and Q=S3
extensionφ:Q→Out NdρLabelID
(C7×Q8)⋊1S3 = Q8⋊D21φ: S3/C1S3 ⊆ Out C7×Q8564+(C7xQ8):1S3336,119
(C7×Q8)⋊2S3 = C7×GL2(𝔽3)φ: S3/C1S3 ⊆ Out C7×Q8562(C7xQ8):2S3336,116
(C7×Q8)⋊3S3 = Q82D21φ: S3/C3C2 ⊆ Out C7×Q81684+(C7xQ8):3S3336,103
(C7×Q8)⋊4S3 = Q8×D21φ: S3/C3C2 ⊆ Out C7×Q81684-(C7xQ8):4S3336,200
(C7×Q8)⋊5S3 = Q83D21φ: S3/C3C2 ⊆ Out C7×Q81684+(C7xQ8):5S3336,201
(C7×Q8)⋊6S3 = C7×Q82S3φ: S3/C3C2 ⊆ Out C7×Q81684(C7xQ8):6S3336,87
(C7×Q8)⋊7S3 = C7×Q83S3φ: trivial image1684(C7xQ8):7S3336,191

Non-split extensions G=N.Q with N=C7×Q8 and Q=S3
extensionφ:Q→Out NdρLabelID
(C7×Q8).1S3 = Q8.D21φ: S3/C1S3 ⊆ Out C7×Q81124-(C7xQ8).1S3336,118
(C7×Q8).2S3 = C7×CSU2(𝔽3)φ: S3/C1S3 ⊆ Out C7×Q81122(C7xQ8).2S3336,115
(C7×Q8).3S3 = C217Q16φ: S3/C3C2 ⊆ Out C7×Q83364-(C7xQ8).3S3336,104
(C7×Q8).4S3 = C7×C3⋊Q16φ: S3/C3C2 ⊆ Out C7×Q83364(C7xQ8).4S3336,88

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