# Extensions 1→N→G→Q→1 with N=C3×He3 and Q=C6

Direct product G=N×Q with N=C3×He3 and Q=C6
dρLabelID
C3×C6×He3162C3xC6xHe3486,251

Semidirect products G=N:Q with N=C3×He3 and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×He3)⋊1C6 = C3.C3≀S3φ: C6/C1C6 ⊆ Out C3×He3546(C3xHe3):1C6486,4
(C3×He3)⋊2C6 = C34⋊C6φ: C6/C1C6 ⊆ Out C3×He3186(C3xHe3):2C6486,102
(C3×He3)⋊3C6 = C34⋊S3φ: C6/C1C6 ⊆ Out C3×He327(C3xHe3):3C6486,103
(C3×He3)⋊4C6 = C3×C3≀S3φ: C6/C1C6 ⊆ Out C3×He327(C3xHe3):4C6486,115
(C3×He3)⋊5C6 = S3×C3≀C3φ: C6/C1C6 ⊆ Out C3×He3186(C3xHe3):5C6486,117
(C3×He3)⋊6C6 = S3×He3⋊C3φ: C6/C1C6 ⊆ Out C3×He3546(C3xHe3):6C6486,123
(C3×He3)⋊7C6 = C3≀C3⋊C6φ: C6/C1C6 ⊆ Out C3×He3279(C3xHe3):7C6486,126
(C3×He3)⋊8C6 = (C3×He3)⋊C6φ: C6/C1C6 ⊆ Out C3×He32718+(C3xHe3):8C6486,127
(C3×He3)⋊9C6 = C343S3φ: C6/C1C6 ⊆ Out C3×He3186(C3xHe3):9C6486,145
(C3×He3)⋊10C6 = C345S3φ: C6/C1C6 ⊆ Out C3×He3186(C3xHe3):10C6486,166
(C3×He3)⋊11C6 = 3+ 1+4⋊C2φ: C6/C1C6 ⊆ Out C3×He32718+(C3xHe3):11C6486,236
(C3×He3)⋊12C6 = 3+ 1+42C2φ: C6/C1C6 ⊆ Out C3×He3279(C3xHe3):12C6486,237
(C3×He3)⋊13C6 = C2×C32.24He3φ: C6/C2C3 ⊆ Out C3×He3162(C3xHe3):13C6486,63
(C3×He3)⋊14C6 = C2×C32⋊He3φ: C6/C2C3 ⊆ Out C3×He354(C3xHe3):14C6486,196
(C3×He3)⋊15C6 = C6×C3≀C3φ: C6/C2C3 ⊆ Out C3×He354(C3xHe3):15C6486,210
(C3×He3)⋊16C6 = C6×He3⋊C3φ: C6/C2C3 ⊆ Out C3×He3162(C3xHe3):16C6486,212
(C3×He3)⋊17C6 = C2×C33⋊C32φ: C6/C2C3 ⊆ Out C3×He3549(C3xHe3):17C6486,215
(C3×He3)⋊18C6 = C2×He3⋊C32φ: C6/C2C3 ⊆ Out C3×He3549(C3xHe3):18C6486,217
(C3×He3)⋊19C6 = C2×3+ 1+4φ: C6/C2C3 ⊆ Out C3×He3549(C3xHe3):19C6486,254
(C3×He3)⋊20C6 = C32×C32⋊C6φ: C6/C3C2 ⊆ Out C3×He354(C3xHe3):20C6486,222
(C3×He3)⋊21C6 = C3×S3×He3φ: C6/C3C2 ⊆ Out C3×He354(C3xHe3):21C6486,223
(C3×He3)⋊22C6 = C3×He34S3φ: C6/C3C2 ⊆ Out C3×He354(C3xHe3):22C6486,229
(C3×He3)⋊23C6 = C32×He3⋊C2φ: C6/C3C2 ⊆ Out C3×He381(C3xHe3):23C6486,230
(C3×He3)⋊24C6 = C3×He35S3φ: C6/C3C2 ⊆ Out C3×He354(C3xHe3):24C6486,243

Non-split extensions G=N.Q with N=C3×He3 and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×He3).1C6 = C32⋊C9⋊S3φ: C6/C1C6 ⊆ Out C3×He3186(C3xHe3).1C6486,7
(C3×He3).2C6 = (C3×He3).C6φ: C6/C1C6 ⊆ Out C3×He3546(C3xHe3).2C6486,9
(C3×He3).3C6 = He3⋊C18φ: C6/C1C6 ⊆ Out C3×He381(C3xHe3).3C6486,24
(C3×He3).4C6 = C9⋊He3⋊C2φ: C6/C1C6 ⊆ Out C3×He3546(C3xHe3).4C6486,107
(C3×He3).5C6 = C3×He3.C6φ: C6/C1C6 ⊆ Out C3×He381(C3xHe3).5C6486,118
(C3×He3).6C6 = S3×He3.C3φ: C6/C1C6 ⊆ Out C3×He3546(C3xHe3).6C6486,120
(C3×He3).7C6 = C3×He3.2C6φ: C6/C1C6 ⊆ Out C3×He381(C3xHe3).7C6486,121
(C3×He3).8C6 = He3.C3⋊C6φ: C6/C1C6 ⊆ Out C3×He3279(C3xHe3).8C6486,128
(C3×He3).9C6 = He3.(C3×C6)φ: C6/C1C6 ⊆ Out C3×He3279(C3xHe3).9C6486,130
(C3×He3).10C6 = (C32×C9)⋊8S3φ: C6/C1C6 ⊆ Out C3×He3546(C3xHe3).10C6486,150
(C3×He3).11C6 = He3.C3⋊S3φ: C6/C1C6 ⊆ Out C3×He3546(C3xHe3).11C6486,169
(C3×He3).12C6 = He3⋊C32S3φ: C6/C1C6 ⊆ Out C3×He3546(C3xHe3).12C6486,172
(C3×He3).13C6 = 3- 1+42C2φ: C6/C1C6 ⊆ Out C3×He3279(C3xHe3).13C6486,239
(C3×He3).14C6 = C2×C33.C32φ: C6/C2C3 ⊆ Out C3×He3162(C3xHe3).14C6486,64
(C3×He3).15C6 = C2×C32.27He3φ: C6/C2C3 ⊆ Out C3×He3162(C3xHe3).15C6486,66
(C3×He3).16C6 = C2×He3⋊C9φ: C6/C2C3 ⊆ Out C3×He3162(C3xHe3).16C6486,77
(C3×He3).17C6 = C2×C9⋊He3φ: C6/C2C3 ⊆ Out C3×He3162(C3xHe3).17C6486,198
(C3×He3).18C6 = C2×C32.23C33φ: C6/C2C3 ⊆ Out C3×He3162(C3xHe3).18C6486,199
(C3×He3).19C6 = C6×He3.C3φ: C6/C2C3 ⊆ Out C3×He3162(C3xHe3).19C6486,211
(C3×He3).20C6 = C2×He3.C32φ: C6/C2C3 ⊆ Out C3×He3549(C3xHe3).20C6486,216
(C3×He3).21C6 = C2×3- 1+4φ: C6/C2C3 ⊆ Out C3×He3549(C3xHe3).21C6486,255
(C3×He3).22C6 = C9×C32⋊C6φ: C6/C3C2 ⊆ Out C3×He3546(C3xHe3).22C6486,98
(C3×He3).23C6 = C9×He3⋊C2φ: C6/C3C2 ⊆ Out C3×He381(C3xHe3).23C6486,143
(C3×He3).24C6 = S3×C9○He3φ: C6/C3C2 ⊆ Out C3×He3546(C3xHe3).24C6486,226
(C3×He3).25C6 = C3×He3.4C6φ: C6/C3C2 ⊆ Out C3×He381(C3xHe3).25C6486,235
(C3×He3).26C6 = C9○He34S3φ: C6/C3C2 ⊆ Out C3×He3546(C3xHe3).26C6486,246
(C3×He3).27C6 = C18×He3φ: trivial image162(C3xHe3).27C6486,194
(C3×He3).28C6 = C6×C9○He3φ: trivial image162(C3xHe3).28C6486,253

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