# Extensions 1→N→G→Q→1 with N=C3×SL2(𝔽3) and Q=C6

Direct product G=N×Q with N=C3×SL2(𝔽3) and Q=C6
dρLabelID
C3×C6×SL2(𝔽3)144C3xC6xSL(2,3)432,698

Semidirect products G=N:Q with N=C3×SL2(𝔽3) and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×SL2(𝔽3))⋊C6 = C322GL2(𝔽3)φ: C6/C1C6 ⊆ Out C3×SL2(𝔽3)7212+(C3xSL(2,3)):C6432,248
(C3×SL2(𝔽3))⋊2C6 = C2×Q8⋊He3φ: C6/C2C3 ⊆ Out C3×SL2(𝔽3)144(C3xSL(2,3)):2C6432,336
(C3×SL2(𝔽3))⋊3C6 = C4○D4⋊He3φ: C6/C2C3 ⊆ Out C3×SL2(𝔽3)726(C3xSL(2,3)):3C6432,339
(C3×SL2(𝔽3))⋊4C6 = C3×C6.6S4φ: C6/C3C2 ⊆ Out C3×SL2(𝔽3)484(C3xSL(2,3)):4C6432,617
(C3×SL2(𝔽3))⋊5C6 = C3×Dic3.A4φ: C6/C3C2 ⊆ Out C3×SL2(𝔽3)484(C3xSL(2,3)):5C6432,622
(C3×SL2(𝔽3))⋊6C6 = C3×S3×SL2(𝔽3)φ: C6/C3C2 ⊆ Out C3×SL2(𝔽3)484(C3xSL(2,3)):6C6432,623
(C3×SL2(𝔽3))⋊7C6 = C32×GL2(𝔽3)φ: C6/C3C2 ⊆ Out C3×SL2(𝔽3)72(C3xSL(2,3)):7C6432,614
(C3×SL2(𝔽3))⋊8C6 = C32×C4.A4φ: trivial image144(C3xSL(2,3)):8C6432,699

Non-split extensions G=N.Q with N=C3×SL2(𝔽3) and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×SL2(𝔽3)).C6 = C32⋊CSU2(𝔽3)φ: C6/C1C6 ⊆ Out C3×SL2(𝔽3)14412-(C3xSL(2,3)).C6432,247
(C3×SL2(𝔽3)).2C6 = C2×C18.A4φ: C6/C2C3 ⊆ Out C3×SL2(𝔽3)144(C3xSL(2,3)).2C6432,328
(C3×SL2(𝔽3)).3C6 = C36.A4φ: C6/C2C3 ⊆ Out C3×SL2(𝔽3)1446(C3xSL(2,3)).3C6432,330
(C3×SL2(𝔽3)).4C6 = C3×C6.5S4φ: C6/C3C2 ⊆ Out C3×SL2(𝔽3)484(C3xSL(2,3)).4C6432,616
(C3×SL2(𝔽3)).5C6 = C9×CSU2(𝔽3)φ: C6/C3C2 ⊆ Out C3×SL2(𝔽3)1442(C3xSL(2,3)).5C6432,240
(C3×SL2(𝔽3)).6C6 = C9×GL2(𝔽3)φ: C6/C3C2 ⊆ Out C3×SL2(𝔽3)722(C3xSL(2,3)).6C6432,241
(C3×SL2(𝔽3)).7C6 = C32×CSU2(𝔽3)φ: C6/C3C2 ⊆ Out C3×SL2(𝔽3)144(C3xSL(2,3)).7C6432,613
(C3×SL2(𝔽3)).8C6 = C18×SL2(𝔽3)φ: trivial image144(C3xSL(2,3)).8C6432,327
(C3×SL2(𝔽3)).9C6 = C9×C4.A4φ: trivial image1442(C3xSL(2,3)).9C6432,329

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