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Extensions 1→N→G→Q→1 with N=Q8xC32 and Q=S3

Direct product G=NxQ with N=Q8xC32 and Q=S3
dρLabelID
S3xQ8xC32144S3xQ8xC3^2432,706

Semidirect products G=N:Q with N=Q8xC32 and Q=S3
extensionφ:Q→Out NdρLabelID
(Q8xC32):1S3 = He3:10SD16φ: S3/C1 → S3 ⊆ Out Q8xC327212+(Q8xC3^2):1S3432,161
(Q8xC32):2S3 = He3:11SD16φ: S3/C1 → S3 ⊆ Out Q8xC32726(Q8xC3^2):2S3432,196
(Q8xC32):3S3 = C32:2GL2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC327212+(Q8xC3^2):3S3432,248
(Q8xC32):4S3 = C32:3GL2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC32726(Q8xC3^2):4S3432,258
(Q8xC32):5S3 = Q8xC32:C6φ: S3/C1 → S3 ⊆ Out Q8xC327212-(Q8xC3^2):5S3432,368
(Q8xC32):6S3 = (Q8xHe3):C2φ: S3/C1 → S3 ⊆ Out Q8xC327212+(Q8xC3^2):6S3432,369
(Q8xC32):7S3 = Q8xHe3:C2φ: S3/C1 → S3 ⊆ Out Q8xC32726(Q8xC3^2):7S3432,394
(Q8xC32):8S3 = He3:5D4:C2φ: S3/C1 → S3 ⊆ Out Q8xC32726(Q8xC3^2):8S3432,395
(Q8xC32):9S3 = C3xC6.6S4φ: S3/C1 → S3 ⊆ Out Q8xC32484(Q8xC3^2):9S3432,617
(Q8xC32):10S3 = C32:5GL2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC3272(Q8xC3^2):10S3432,620
(Q8xC32):11S3 = C32xGL2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC3272(Q8xC3^2):11S3432,614
(Q8xC32):12S3 = C3xC32:11SD16φ: S3/C3 → C2 ⊆ Out Q8xC32144(Q8xC3^2):12S3432,493
(Q8xC32):13S3 = C33:27SD16φ: S3/C3 → C2 ⊆ Out Q8xC32216(Q8xC3^2):13S3432,509
(Q8xC32):14S3 = C3xQ8xC3:S3φ: S3/C3 → C2 ⊆ Out Q8xC32144(Q8xC3^2):14S3432,716
(Q8xC32):15S3 = C3xC12.26D6φ: S3/C3 → C2 ⊆ Out Q8xC32144(Q8xC3^2):15S3432,717
(Q8xC32):16S3 = Q8xC33:C2φ: S3/C3 → C2 ⊆ Out Q8xC32216(Q8xC3^2):16S3432,726
(Q8xC32):17S3 = (Q8xC33):C2φ: S3/C3 → C2 ⊆ Out Q8xC32216(Q8xC3^2):17S3432,727
(Q8xC32):18S3 = C32xQ8:2S3φ: S3/C3 → C2 ⊆ Out Q8xC32144(Q8xC3^2):18S3432,477
(Q8xC32):19S3 = C32xQ8:3S3φ: trivial image144(Q8xC3^2):19S3432,707

Non-split extensions G=N.Q with N=Q8xC32 and Q=S3
extensionφ:Q→Out NdρLabelID
(Q8xC32).1S3 = He3:6Q16φ: S3/C1 → S3 ⊆ Out Q8xC3214412-(Q8xC3^2).1S3432,160
(Q8xC32).2S3 = Dic18.C6φ: S3/C1 → S3 ⊆ Out Q8xC3214412-(Q8xC3^2).2S3432,162
(Q8xC32).3S3 = D36.C6φ: S3/C1 → S3 ⊆ Out Q8xC327212+(Q8xC3^2).3S3432,163
(Q8xC32).4S3 = He3:7Q16φ: S3/C1 → S3 ⊆ Out Q8xC321446(Q8xC3^2).4S3432,197
(Q8xC32).5S3 = C32.CSU2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC3214412-(Q8xC3^2).5S3432,243
(Q8xC32).6S3 = C3xQ8.D9φ: S3/C1 → S3 ⊆ Out Q8xC321444(Q8xC3^2).6S3432,244
(Q8xC32).7S3 = C32.GL2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC327212+(Q8xC3^2).7S3432,245
(Q8xC32).8S3 = C3xQ8:D9φ: S3/C1 → S3 ⊆ Out Q8xC321444(Q8xC3^2).8S3432,246
(Q8xC32).9S3 = C32:CSU2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC3214412-(Q8xC3^2).9S3432,247
(Q8xC32).10S3 = C32.3CSU2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC32432(Q8xC3^2).10S3432,255
(Q8xC32).11S3 = C32.3GL2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC32216(Q8xC3^2).11S3432,256
(Q8xC32).12S3 = C32:2CSU2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC321446(Q8xC3^2).12S3432,257
(Q8xC32).13S3 = Q8xC9:C6φ: S3/C1 → S3 ⊆ Out Q8xC327212-(Q8xC3^2).13S3432,370
(Q8xC32).14S3 = D36:3C6φ: S3/C1 → S3 ⊆ Out Q8xC327212+(Q8xC3^2).14S3432,371
(Q8xC32).15S3 = C3xC6.5S4φ: S3/C1 → S3 ⊆ Out Q8xC32484(Q8xC3^2).15S3432,616
(Q8xC32).16S3 = C32:4CSU2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC32144(Q8xC3^2).16S3432,619
(Q8xC32).17S3 = C32xCSU2(F3)φ: S3/C1 → S3 ⊆ Out Q8xC32144(Q8xC3^2).17S3432,613
(Q8xC32).18S3 = C3xC9:Q16φ: S3/C3 → C2 ⊆ Out Q8xC321444(Q8xC3^2).18S3432,156
(Q8xC32).19S3 = C3xQ8:2D9φ: S3/C3 → C2 ⊆ Out Q8xC321444(Q8xC3^2).19S3432,157
(Q8xC32).20S3 = C36.19D6φ: S3/C3 → C2 ⊆ Out Q8xC32432(Q8xC3^2).20S3432,194
(Q8xC32).21S3 = C36.20D6φ: S3/C3 → C2 ⊆ Out Q8xC32216(Q8xC3^2).21S3432,195
(Q8xC32).22S3 = C3xQ8xD9φ: S3/C3 → C2 ⊆ Out Q8xC321444(Q8xC3^2).22S3432,364
(Q8xC32).23S3 = C3xQ8:3D9φ: S3/C3 → C2 ⊆ Out Q8xC321444(Q8xC3^2).23S3432,365
(Q8xC32).24S3 = Q8xC9:S3φ: S3/C3 → C2 ⊆ Out Q8xC32216(Q8xC3^2).24S3432,392
(Q8xC32).25S3 = C36.29D6φ: S3/C3 → C2 ⊆ Out Q8xC32216(Q8xC3^2).25S3432,393
(Q8xC32).26S3 = C3xC32:7Q16φ: S3/C3 → C2 ⊆ Out Q8xC32144(Q8xC3^2).26S3432,494
(Q8xC32).27S3 = C33:15Q16φ: S3/C3 → C2 ⊆ Out Q8xC32432(Q8xC3^2).27S3432,510
(Q8xC32).28S3 = C32xC3:Q16φ: S3/C3 → C2 ⊆ Out Q8xC32144(Q8xC3^2).28S3432,478

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