# Extensions 1→N→G→Q→1 with N=Q8 and Q=S32

Direct product G=N×Q with N=Q8 and Q=S32
dρLabelID
S32×Q8488-S3^2xQ8288,965

Semidirect products G=N:Q with N=Q8 and Q=S32
extensionφ:Q→Out NdρLabelID
Q8⋊S32 = S3×GL2(𝔽3)φ: S32/S3S3 ⊆ Out Q8244Q8:S3^2288,851
Q82S32 = S3×Q82S3φ: S32/C3×S3C2 ⊆ Out Q8488+Q8:2S3^2288,586
Q83S32 = D126D6φ: S32/C3×S3C2 ⊆ Out Q8488+Q8:3S3^2288,587
Q84S32 = D12.9D6φ: S32/C3⋊S3C2 ⊆ Out Q8488-Q8:4S3^2288,588
Q85S32 = D12.10D6φ: S32/C3⋊S3C2 ⊆ Out Q8488+Q8:5S3^2288,589
Q86S32 = S3×Q83S3φ: trivial image488+Q8:6S3^2288,966
Q87S32 = D1215D6φ: trivial image488-Q8:7S3^2288,967
Q88S32 = D1216D6φ: trivial image488+Q8:8S3^2288,968

Non-split extensions G=N.Q with N=Q8 and Q=S32
extensionφ:Q→Out NdρLabelID
Q8.1S32 = CSU2(𝔽3)⋊S3φ: S32/S3S3 ⊆ Out Q8964Q8.1S3^2288,844
Q8.2S32 = Dic3.4S4φ: S32/S3S3 ⊆ Out Q8484Q8.2S3^2288,845
Q8.3S32 = Dic3.5S4φ: S32/S3S3 ⊆ Out Q8484+Q8.3S3^2288,846
Q8.4S32 = GL2(𝔽3)⋊S3φ: S32/S3S3 ⊆ Out Q8484+Q8.4S3^2288,847
Q8.5S32 = S3×CSU2(𝔽3)φ: S32/S3S3 ⊆ Out Q8484-Q8.5S3^2288,848
Q8.6S32 = D6.S4φ: S32/S3S3 ⊆ Out Q8484-Q8.6S3^2288,849
Q8.7S32 = D6.2S4φ: S32/S3S3 ⊆ Out Q8484Q8.7S3^2288,850
Q8.8S32 = S3×C3⋊Q16φ: S32/C3×S3C2 ⊆ Out Q8968-Q8.8S3^2288,590
Q8.9S32 = D12.11D6φ: S32/C3×S3C2 ⊆ Out Q8968-Q8.9S3^2288,591
Q8.10S32 = D12.24D6φ: S32/C3×S3C2 ⊆ Out Q8968-Q8.10S3^2288,594
Q8.11S32 = D12.12D6φ: S32/C3×S3C2 ⊆ Out Q8968-Q8.11S3^2288,595
Q8.12S32 = Dic6.22D6φ: S32/C3×S3C2 ⊆ Out Q8488+Q8.12S3^2288,596
Q8.13S32 = D12.13D6φ: S32/C3×S3C2 ⊆ Out Q8488+Q8.13S3^2288,597
Q8.14S32 = Dic6.9D6φ: S32/C3⋊S3C2 ⊆ Out Q8488-Q8.14S3^2288,592
Q8.15S32 = Dic6.10D6φ: S32/C3⋊S3C2 ⊆ Out Q8488+Q8.15S3^2288,593
Q8.16S32 = D12.14D6φ: S32/C3⋊S3C2 ⊆ Out Q8488+Q8.16S3^2288,598
Q8.17S32 = D12.15D6φ: S32/C3⋊S3C2 ⊆ Out Q8488-Q8.17S3^2288,599
Q8.18S32 = D12.25D6φ: trivial image488-Q8.18S3^2288,963
Q8.19S32 = Dic6.26D6φ: trivial image488+Q8.19S3^2288,964

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