# Extensions 1→N→G→Q→1 with N=C2×Q8 and Q=C3⋊S3

Direct product G=N×Q with N=C2×Q8 and Q=C3⋊S3
dρLabelID
C2×Q8×C3⋊S3144C2xQ8xC3:S3288,1010

Semidirect products G=N:Q with N=C2×Q8 and Q=C3⋊S3
extensionφ:Q→Out NdρLabelID
(C2×Q8)⋊1(C3⋊S3) = C2×C6.6S4φ: C3⋊S3/C3S3 ⊆ Out C2×Q848(C2xQ8):1(C3:S3)288,911
(C2×Q8)⋊2(C3⋊S3) = SL2(𝔽3).D6φ: C3⋊S3/C3S3 ⊆ Out C2×Q8484(C2xQ8):2(C3:S3)288,912
(C2×Q8)⋊3(C3⋊S3) = C2×C3211SD16φ: C3⋊S3/C32C2 ⊆ Out C2×Q8144(C2xQ8):3(C3:S3)288,798
(C2×Q8)⋊4(C3⋊S3) = C62.134D4φ: C3⋊S3/C32C2 ⊆ Out C2×Q8144(C2xQ8):4(C3:S3)288,799
(C2×Q8)⋊5(C3⋊S3) = C62.261C23φ: C3⋊S3/C32C2 ⊆ Out C2×Q8144(C2xQ8):5(C3:S3)288,803
(C2×Q8)⋊6(C3⋊S3) = C62.262C23φ: C3⋊S3/C32C2 ⊆ Out C2×Q8144(C2xQ8):6(C3:S3)288,804
(C2×Q8)⋊7(C3⋊S3) = C3272- 1+4φ: C3⋊S3/C32C2 ⊆ Out C2×Q8144(C2xQ8):7(C3:S3)288,1012
(C2×Q8)⋊8(C3⋊S3) = C2×C12.26D6φ: trivial image144(C2xQ8):8(C3:S3)288,1011

Non-split extensions G=N.Q with N=C2×Q8 and Q=C3⋊S3
extensionφ:Q→Out NdρLabelID
(C2×Q8).1(C3⋊S3) = C6.GL2(𝔽3)φ: C3⋊S3/C3S3 ⊆ Out C2×Q896(C2xQ8).1(C3:S3)288,403
(C2×Q8).2(C3⋊S3) = C2×C6.5S4φ: C3⋊S3/C3S3 ⊆ Out C2×Q896(C2xQ8).2(C3:S3)288,910
(C2×Q8).3(C3⋊S3) = C62.117D4φ: C3⋊S3/C32C2 ⊆ Out C2×Q8288(C2xQ8).3(C3:S3)288,310
(C2×Q8).4(C3⋊S3) = (C6×C12).C4φ: C3⋊S3/C32C2 ⊆ Out C2×Q8144(C2xQ8).4(C3:S3)288,311
(C2×Q8).5(C3⋊S3) = C2×C327Q16φ: C3⋊S3/C32C2 ⊆ Out C2×Q8288(C2xQ8).5(C3:S3)288,800
(C2×Q8).6(C3⋊S3) = C62.259C23φ: C3⋊S3/C32C2 ⊆ Out C2×Q8288(C2xQ8).6(C3:S3)288,801
(C2×Q8).7(C3⋊S3) = Q8×C3⋊Dic3φ: trivial image288(C2xQ8).7(C3:S3)288,802

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