# Extensions 1→N→G→Q→1 with N=Q8×C32 and Q=C6

Direct product G=N×Q with N=Q8×C32 and Q=C6
dρLabelID
Q8×C32×C6432Q8xC3^2xC6432,732

Semidirect products G=N:Q with N=Q8×C32 and Q=C6
extensionφ:Q→Out NdρLabelID
(Q8×C32)⋊1C6 = He310SD16φ: C6/C1C6 ⊆ Out Q8×C327212+(Q8xC3^2):1C6432,161
(Q8×C32)⋊2C6 = Q8⋊He3⋊C2φ: C6/C1C6 ⊆ Out Q8×C327212-(Q8xC3^2):2C6432,270
(Q8×C32)⋊3C6 = Q8×C32⋊C6φ: C6/C1C6 ⊆ Out Q8×C327212-(Q8xC3^2):3C6432,368
(Q8×C32)⋊4C6 = (Q8×He3)⋊C2φ: C6/C1C6 ⊆ Out Q8×C327212+(Q8xC3^2):4C6432,369
(Q8×C32)⋊5C6 = C3×S3×SL2(𝔽3)φ: C6/C1C6 ⊆ Out Q8×C32484(Q8xC3^2):5C6432,623
(Q8×C32)⋊6C6 = C3⋊S3×SL2(𝔽3)φ: C6/C1C6 ⊆ Out Q8×C3272(Q8xC3^2):6C6432,626
(Q8×C32)⋊7C6 = SD16×He3φ: C6/C1C6 ⊆ Out Q8×C32726(Q8xC3^2):7C6432,219
(Q8×C32)⋊8C6 = C2×Q8⋊He3φ: C6/C2C3 ⊆ Out Q8×C32144(Q8xC3^2):8C6432,336
(Q8×C32)⋊9C6 = C2×Q8×He3φ: C6/C2C3 ⊆ Out Q8×C32144(Q8xC3^2):9C6432,407
(Q8×C32)⋊10C6 = C4○D4×He3φ: C6/C2C3 ⊆ Out Q8×C32726(Q8xC3^2):10C6432,410
(Q8×C32)⋊11C6 = C3×C6×SL2(𝔽3)φ: C6/C2C3 ⊆ Out Q8×C32144(Q8xC3^2):11C6432,698
(Q8×C32)⋊12C6 = C32×Q82S3φ: C6/C3C2 ⊆ Out Q8×C32144(Q8xC3^2):12C6432,477
(Q8×C32)⋊13C6 = C3×C3211SD16φ: C6/C3C2 ⊆ Out Q8×C32144(Q8xC3^2):13C6432,493
(Q8×C32)⋊14C6 = S3×Q8×C32φ: C6/C3C2 ⊆ Out Q8×C32144(Q8xC3^2):14C6432,706
(Q8×C32)⋊15C6 = C32×Q83S3φ: C6/C3C2 ⊆ Out Q8×C32144(Q8xC3^2):15C6432,707
(Q8×C32)⋊16C6 = C3×Q8×C3⋊S3φ: C6/C3C2 ⊆ Out Q8×C32144(Q8xC3^2):16C6432,716
(Q8×C32)⋊17C6 = C3×C12.26D6φ: C6/C3C2 ⊆ Out Q8×C32144(Q8xC3^2):17C6432,717
(Q8×C32)⋊18C6 = SD16×C33φ: C6/C3C2 ⊆ Out Q8×C32216(Q8xC3^2):18C6432,518
(Q8×C32)⋊19C6 = C4○D4×C33φ: trivial image216(Q8xC3^2):19C6432,733

Non-split extensions G=N.Q with N=Q8×C32 and Q=C6
extensionφ:Q→Out NdρLabelID
(Q8×C32).1C6 = He36Q16φ: C6/C1C6 ⊆ Out Q8×C3214412-(Q8xC3^2).1C6432,160
(Q8×C32).2C6 = Q8⋊C93S3φ: C6/C1C6 ⊆ Out Q8×C321444(Q8xC3^2).2C6432,267
(Q8×C32).3C6 = S3×Q8⋊C9φ: C6/C1C6 ⊆ Out Q8×C321444(Q8xC3^2).3C6432,268
(Q8×C32).4C6 = C6.(S3×A4)φ: C6/C1C6 ⊆ Out Q8×C327212+(Q8xC3^2).4C6432,269
(Q8×C32).5C6 = C3×Dic3.A4φ: C6/C1C6 ⊆ Out Q8×C32484(Q8xC3^2).5C6432,622
(Q8×C32).6C6 = C3⋊Dic3.2A4φ: C6/C1C6 ⊆ Out Q8×C32144(Q8xC3^2).6C6432,625
(Q8×C32).7C6 = SD16×3- 1+2φ: C6/C1C6 ⊆ Out Q8×C32726(Q8xC3^2).7C6432,220
(Q8×C32).8C6 = Q16×He3φ: C6/C1C6 ⊆ Out Q8×C321446(Q8xC3^2).8C6432,222
(Q8×C32).9C6 = Q16×3- 1+2φ: C6/C1C6 ⊆ Out Q8×C321446(Q8xC3^2).9C6432,223
(Q8×C32).10C6 = C6×Q8⋊C9φ: C6/C2C3 ⊆ Out Q8×C32432(Q8xC3^2).10C6432,334
(Q8×C32).11C6 = C2×Q8⋊3- 1+2φ: C6/C2C3 ⊆ Out Q8×C32144(Q8xC3^2).11C6432,335
(Q8×C32).12C6 = C3×Q8.C18φ: C6/C2C3 ⊆ Out Q8×C32216(Q8xC3^2).12C6432,337
(Q8×C32).13C6 = Q8⋊C94C6φ: C6/C2C3 ⊆ Out Q8×C32726(Q8xC3^2).13C6432,338
(Q8×C32).14C6 = C4○D4⋊He3φ: C6/C2C3 ⊆ Out Q8×C32726(Q8xC3^2).14C6432,339
(Q8×C32).15C6 = C2×Q8×3- 1+2φ: C6/C2C3 ⊆ Out Q8×C32144(Q8xC3^2).15C6432,408
(Q8×C32).16C6 = C4○D4×3- 1+2φ: C6/C2C3 ⊆ Out Q8×C32726(Q8xC3^2).16C6432,411
(Q8×C32).17C6 = C32×C4.A4φ: C6/C2C3 ⊆ Out Q8×C32144(Q8xC3^2).17C6432,699
(Q8×C32).18C6 = C9×Q82S3φ: C6/C3C2 ⊆ Out Q8×C321444(Q8xC3^2).18C6432,158
(Q8×C32).19C6 = C9×C3⋊Q16φ: C6/C3C2 ⊆ Out Q8×C321444(Q8xC3^2).19C6432,159
(Q8×C32).20C6 = S3×Q8×C9φ: C6/C3C2 ⊆ Out Q8×C321444(Q8xC3^2).20C6432,366
(Q8×C32).21C6 = C9×Q83S3φ: C6/C3C2 ⊆ Out Q8×C321444(Q8xC3^2).21C6432,367
(Q8×C32).22C6 = C32×C3⋊Q16φ: C6/C3C2 ⊆ Out Q8×C32144(Q8xC3^2).22C6432,478
(Q8×C32).23C6 = C3×C327Q16φ: C6/C3C2 ⊆ Out Q8×C32144(Q8xC3^2).23C6432,494
(Q8×C32).24C6 = SD16×C3×C9φ: C6/C3C2 ⊆ Out Q8×C32216(Q8xC3^2).24C6432,218
(Q8×C32).25C6 = Q16×C3×C9φ: C6/C3C2 ⊆ Out Q8×C32432(Q8xC3^2).25C6432,221
(Q8×C32).26C6 = Q16×C33φ: C6/C3C2 ⊆ Out Q8×C32432(Q8xC3^2).26C6432,519
(Q8×C32).27C6 = Q8×C3×C18φ: trivial image432(Q8xC3^2).27C6432,406
(Q8×C32).28C6 = C4○D4×C3×C9φ: trivial image216(Q8xC3^2).28C6432,409

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