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

Direct product G=N×Q with N=C3×Q8 and Q=C3⋊S3
dρLabelID
C3×Q8×C3⋊S3144C3xQ8xC3:S3432,716

Semidirect products G=N:Q with N=C3×Q8 and Q=C3⋊S3
extensionφ:Q→Out NdρLabelID
(C3×Q8)⋊1(C3⋊S3) = C325GL2(𝔽3)φ: C3⋊S3/C3S3 ⊆ Out C3×Q872(C3xQ8):1(C3:S3)432,620
(C3×Q8)⋊2(C3⋊S3) = C3×C6.6S4φ: C3⋊S3/C3S3 ⊆ Out C3×Q8484(C3xQ8):2(C3:S3)432,617
(C3×Q8)⋊3(C3⋊S3) = C3327SD16φ: C3⋊S3/C32C2 ⊆ Out C3×Q8216(C3xQ8):3(C3:S3)432,509
(C3×Q8)⋊4(C3⋊S3) = Q8×C33⋊C2φ: C3⋊S3/C32C2 ⊆ Out C3×Q8216(C3xQ8):4(C3:S3)432,726
(C3×Q8)⋊5(C3⋊S3) = (Q8×C33)⋊C2φ: C3⋊S3/C32C2 ⊆ Out C3×Q8216(C3xQ8):5(C3:S3)432,727
(C3×Q8)⋊6(C3⋊S3) = C3×C3211SD16φ: C3⋊S3/C32C2 ⊆ Out C3×Q8144(C3xQ8):6(C3:S3)432,493
(C3×Q8)⋊7(C3⋊S3) = C3×C12.26D6φ: trivial image144(C3xQ8):7(C3:S3)432,717

Non-split extensions G=N.Q with N=C3×Q8 and Q=C3⋊S3
extensionφ:Q→Out NdρLabelID
(C3×Q8).1(C3⋊S3) = C18.5S4φ: C3⋊S3/C3S3 ⊆ Out C3×Q81444-(C3xQ8).1(C3:S3)432,252
(C3×Q8).2(C3⋊S3) = C18.6S4φ: C3⋊S3/C3S3 ⊆ Out C3×Q8724+(C3xQ8).2(C3:S3)432,253
(C3×Q8).3(C3⋊S3) = C32.3CSU2(𝔽3)φ: C3⋊S3/C3S3 ⊆ Out C3×Q8432(C3xQ8).3(C3:S3)432,255
(C3×Q8).4(C3⋊S3) = C32.3GL2(𝔽3)φ: C3⋊S3/C3S3 ⊆ Out C3×Q8216(C3xQ8).4(C3:S3)432,256
(C3×Q8).5(C3⋊S3) = C324CSU2(𝔽3)φ: C3⋊S3/C3S3 ⊆ Out C3×Q8144(C3xQ8).5(C3:S3)432,619
(C3×Q8).6(C3⋊S3) = C322CSU2(𝔽3)φ: C3⋊S3/C3S3 ⊆ Out C3×Q81446(C3xQ8).6(C3:S3)432,257
(C3×Q8).7(C3⋊S3) = C323GL2(𝔽3)φ: C3⋊S3/C3S3 ⊆ Out C3×Q8726(C3xQ8).7(C3:S3)432,258
(C3×Q8).8(C3⋊S3) = C3×C6.5S4φ: C3⋊S3/C3S3 ⊆ Out C3×Q8484(C3xQ8).8(C3:S3)432,616
(C3×Q8).9(C3⋊S3) = C36.19D6φ: C3⋊S3/C32C2 ⊆ Out C3×Q8432(C3xQ8).9(C3:S3)432,194
(C3×Q8).10(C3⋊S3) = C36.20D6φ: C3⋊S3/C32C2 ⊆ Out C3×Q8216(C3xQ8).10(C3:S3)432,195
(C3×Q8).11(C3⋊S3) = Q8×C9⋊S3φ: C3⋊S3/C32C2 ⊆ Out C3×Q8216(C3xQ8).11(C3:S3)432,392
(C3×Q8).12(C3⋊S3) = C36.29D6φ: C3⋊S3/C32C2 ⊆ Out C3×Q8216(C3xQ8).12(C3:S3)432,393
(C3×Q8).13(C3⋊S3) = C3315Q16φ: C3⋊S3/C32C2 ⊆ Out C3×Q8432(C3xQ8).13(C3:S3)432,510
(C3×Q8).14(C3⋊S3) = He311SD16φ: C3⋊S3/C32C2 ⊆ Out C3×Q8726(C3xQ8).14(C3:S3)432,196
(C3×Q8).15(C3⋊S3) = He37Q16φ: C3⋊S3/C32C2 ⊆ Out C3×Q81446(C3xQ8).15(C3:S3)432,197
(C3×Q8).16(C3⋊S3) = C3×C327Q16φ: C3⋊S3/C32C2 ⊆ Out C3×Q8144(C3xQ8).16(C3:S3)432,494
(C3×Q8).17(C3⋊S3) = Q8×He3⋊C2φ: trivial image726(C3xQ8).17(C3:S3)432,394
(C3×Q8).18(C3⋊S3) = He35D4⋊C2φ: trivial image726(C3xQ8).18(C3:S3)432,395

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