# Extensions 1→N→G→Q→1 with N=C3×3- 1+2 and Q=C6

Direct product G=N×Q with N=C3×3- 1+2 and Q=C6
dρLabelID
C3×C6×3- 1+2162C3xC6xES-(3,1)486,252

Semidirect products G=N:Q with N=C3×3- 1+2 and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×3- 1+2)⋊1C6 = C34.S3φ: C6/C1C6 ⊆ Out C3×3- 1+227(C3xES-(3,1)):1C6486,105
(C3×3- 1+2)⋊2C6 = D9⋊He3φ: C6/C1C6 ⊆ Out C3×3- 1+2546(C3xES-(3,1)):2C6486,106
(C3×3- 1+2)⋊3C6 = C9⋊S3⋊C32φ: C6/C1C6 ⊆ Out C3×3- 1+22718+(C3xES-(3,1)):3C6486,129
(C3×3- 1+2)⋊4C6 = He3.(C3×S3)φ: C6/C1C6 ⊆ Out C3×3- 1+22718+(C3xES-(3,1)):4C6486,131
(C3×3- 1+2)⋊5C6 = 3- 1+4⋊C2φ: C6/C1C6 ⊆ Out C3×3- 1+22718+(C3xES-(3,1)):5C6486,238
(C3×3- 1+2)⋊6C6 = S3×C3≀C3φ: C6/C1C6 ⊆ Out C3×3- 1+2186(C3xES-(3,1)):6C6486,117
(C3×3- 1+2)⋊7C6 = S3×He3.C3φ: C6/C1C6 ⊆ Out C3×3- 1+2546(C3xES-(3,1)):7C6486,120
(C3×3- 1+2)⋊8C6 = C2×C33.C32φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)):8C6486,64
(C3×3- 1+2)⋊9C6 = C2×C34.C3φ: C6/C2C3 ⊆ Out C3×3- 1+254(C3xES-(3,1)):9C6486,197
(C3×3- 1+2)⋊10C6 = C2×C9⋊He3φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)):10C6486,198
(C3×3- 1+2)⋊11C6 = C2×C32.23C33φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)):11C6486,199
(C3×3- 1+2)⋊12C6 = C6×C3≀C3φ: C6/C2C3 ⊆ Out C3×3- 1+254(C3xES-(3,1)):12C6486,210
(C3×3- 1+2)⋊13C6 = C6×He3.C3φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)):13C6486,211
(C3×3- 1+2)⋊14C6 = C2×C33⋊C32φ: C6/C2C3 ⊆ Out C3×3- 1+2549(C3xES-(3,1)):14C6486,215
(C3×3- 1+2)⋊15C6 = C2×He3.C32φ: C6/C2C3 ⊆ Out C3×3- 1+2549(C3xES-(3,1)):15C6486,216
(C3×3- 1+2)⋊16C6 = C2×He3⋊C32φ: C6/C2C3 ⊆ Out C3×3- 1+2549(C3xES-(3,1)):16C6486,217
(C3×3- 1+2)⋊17C6 = C2×C9.2He3φ: C6/C2C3 ⊆ Out C3×3- 1+2549(C3xES-(3,1)):17C6486,219
(C3×3- 1+2)⋊18C6 = C2×3- 1+4φ: C6/C2C3 ⊆ Out C3×3- 1+2549(C3xES-(3,1)):18C6486,255
(C3×3- 1+2)⋊19C6 = C32×C9⋊C6φ: C6/C3C2 ⊆ Out C3×3- 1+254(C3xES-(3,1)):19C6486,224
(C3×3- 1+2)⋊20C6 = C3×C33.S3φ: C6/C3C2 ⊆ Out C3×3- 1+254(C3xES-(3,1)):20C6486,232
(C3×3- 1+2)⋊21C6 = C3×S3×3- 1+2φ: C6/C3C2 ⊆ Out C3×3- 1+254(C3xES-(3,1)):21C6486,225
(C3×3- 1+2)⋊22C6 = S3×C9○He3φ: C6/C3C2 ⊆ Out C3×3- 1+2546(C3xES-(3,1)):22C6486,226
(C3×3- 1+2)⋊23C6 = C6×C9○He3φ: trivial image162(C3xES-(3,1)):23C6486,253

Non-split extensions G=N.Q with N=C3×3- 1+2 and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×3- 1+2).1C6 = C927C6φ: C6/C1C6 ⊆ Out C3×3- 1+2546(C3xES-(3,1)).1C6486,109
(C3×3- 1+2).2C6 = C928C6φ: C6/C1C6 ⊆ Out C3×3- 1+2186(C3xES-(3,1)).2C6486,110
(C3×3- 1+2).3C6 = S3×C3.He3φ: C6/C1C6 ⊆ Out C3×3- 1+2546(C3xES-(3,1)).3C6486,124
(C3×3- 1+2).4C6 = C2×C33.3C32φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)).4C6486,65
(C3×3- 1+2).5C6 = C2×C32.28He3φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)).5C6486,67
(C3×3- 1+2).6C6 = C2×3- 1+2⋊C9φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)).6C6486,78
(C3×3- 1+2).7C6 = C2×C9⋊3- 1+2φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)).7C6486,200
(C3×3- 1+2).8C6 = C2×C927C3φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)).8C6486,202
(C3×3- 1+2).9C6 = C2×C928C3φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)).9C6486,205
(C3×3- 1+2).10C6 = C2×C929C3φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)).10C6486,206
(C3×3- 1+2).11C6 = C6×C3.He3φ: C6/C2C3 ⊆ Out C3×3- 1+2162(C3xES-(3,1)).11C6486,213
(C3×3- 1+2).12C6 = C2×C32.C33φ: C6/C2C3 ⊆ Out C3×3- 1+2549(C3xES-(3,1)).12C6486,218
(C3×3- 1+2).13C6 = C9×C9⋊C6φ: C6/C3C2 ⊆ Out C3×3- 1+2546(C3xES-(3,1)).13C6486,100
(C3×3- 1+2).14C6 = C18×3- 1+2φ: trivial image162(C3xES-(3,1)).14C6486,195

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