# Extensions 1→N→G→Q→1 with N=Q8×C9 and Q=S3

Direct product G=N×Q with N=Q8×C9 and Q=S3
dρLabelID
S3×Q8×C91444S3xQ8xC9432,366

Semidirect products G=N:Q with N=Q8×C9 and Q=S3
extensionφ:Q→Out NdρLabelID
(Q8×C9)⋊1S3 = C18.6S4φ: S3/C1S3 ⊆ Out Q8×C9724+(Q8xC9):1S3432,253
(Q8×C9)⋊2S3 = C9×GL2(𝔽3)φ: S3/C1S3 ⊆ Out Q8×C9722(Q8xC9):2S3432,241
(Q8×C9)⋊3S3 = C36.20D6φ: S3/C3C2 ⊆ Out Q8×C9216(Q8xC9):3S3432,195
(Q8×C9)⋊4S3 = Q8×C9⋊S3φ: S3/C3C2 ⊆ Out Q8×C9216(Q8xC9):4S3432,392
(Q8×C9)⋊5S3 = C36.29D6φ: S3/C3C2 ⊆ Out Q8×C9216(Q8xC9):5S3432,393
(Q8×C9)⋊6S3 = C9×Q82S3φ: S3/C3C2 ⊆ Out Q8×C91444(Q8xC9):6S3432,158
(Q8×C9)⋊7S3 = C9×Q83S3φ: trivial image1444(Q8xC9):7S3432,367

Non-split extensions G=N.Q with N=Q8×C9 and Q=S3
extensionφ:Q→Out NdρLabelID
(Q8×C9).1S3 = Q8.D27φ: S3/C1S3 ⊆ Out Q8×C94324-(Q8xC9).1S3432,37
(Q8×C9).2S3 = Q8⋊D27φ: S3/C1S3 ⊆ Out Q8×C92164+(Q8xC9).2S3432,38
(Q8×C9).3S3 = C18.5S4φ: S3/C1S3 ⊆ Out Q8×C91444-(Q8xC9).3S3432,252
(Q8×C9).4S3 = C9×CSU2(𝔽3)φ: S3/C1S3 ⊆ Out Q8×C91442(Q8xC9).4S3432,240
(Q8×C9).5S3 = C27⋊Q16φ: S3/C3C2 ⊆ Out Q8×C94324-(Q8xC9).5S3432,17
(Q8×C9).6S3 = Q82D27φ: S3/C3C2 ⊆ Out Q8×C92164+(Q8xC9).6S3432,18
(Q8×C9).7S3 = Q8×D27φ: S3/C3C2 ⊆ Out Q8×C92164-(Q8xC9).7S3432,49
(Q8×C9).8S3 = Q83D27φ: S3/C3C2 ⊆ Out Q8×C92164+(Q8xC9).8S3432,50
(Q8×C9).9S3 = C36.19D6φ: S3/C3C2 ⊆ Out Q8×C9432(Q8xC9).9S3432,194
(Q8×C9).10S3 = C9×C3⋊Q16φ: S3/C3C2 ⊆ Out Q8×C91444(Q8xC9).10S3432,159

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