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Extensions 1→N→G→Q→1 with N=C7×C4⋊C4 and Q=C4

Direct product G=N×Q with N=C7×C4⋊C4 and Q=C4
dρLabelID
C4⋊C4×C28448C4:C4xC28448,786

Semidirect products G=N:Q with N=C7×C4⋊C4 and Q=C4
extensionφ:Q→Out NdρLabelID
(C7×C4⋊C4)⋊1C4 = (D4×C14)⋊C4φ: C4/C1 → C4 ⊆ Out C7×C4⋊C4112(C7xC4:C4):1C4448,94
(C7×C4⋊C4)⋊2C4 = C4⋊C4⋊Dic7φ: C4/C1 → C4 ⊆ Out C7×C4⋊C4112(C7xC4:C4):2C4448,95
(C7×C4⋊C4)⋊3C4 = C7×C22.SD16φ: C4/C1 → C4 ⊆ Out C7×C4⋊C4112(C7xC4:C4):3C4448,131
(C7×C4⋊C4)⋊4C4 = C7×C23.31D4φ: C4/C1 → C4 ⊆ Out C7×C4⋊C4112(C7xC4:C4):4C4448,132
(C7×C4⋊C4)⋊5C4 = C28.C42φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4):5C4448,86
(C7×C4⋊C4)⋊6C4 = C28.2C42φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4112(C7xC4:C4):6C4448,89
(C7×C4⋊C4)⋊7C4 = C4⋊C4×Dic7φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4):7C4448,509
(C7×C4⋊C4)⋊8C4 = C4⋊C4⋊5Dic7φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4):8C4448,515
(C7×C4⋊C4)⋊9C4 = C4⋊(C4⋊Dic7)φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4):9C4448,519
(C7×C4⋊C4)⋊10C4 = C7×C42⋊6C4φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4112(C7xC4:C4):10C4448,143
(C7×C4⋊C4)⋊11C4 = C7×C22.4Q16φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4):11C4448,144
(C7×C4⋊C4)⋊12C4 = C7×C23.63C23φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4):12C4448,795
(C7×C4⋊C4)⋊13C4 = C7×C23.65C23φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4):13C4448,797

Non-split extensions G=N.Q with N=C7×C4⋊C4 and Q=C4
extensionφ:Q→Out NdρLabelID
(C7×C4⋊C4).1C4 = C42.8D14φ: C4/C1 → C4 ⊆ Out C7×C4⋊C4448(C7xC4:C4).1C4448,100
(C7×C4⋊C4).2C4 = C28.10D8φ: C4/C1 → C4 ⊆ Out C7×C4⋊C4448(C7xC4:C4).2C4448,104
(C7×C4⋊C4).3C4 = C7×C42.2C22φ: C4/C1 → C4 ⊆ Out C7×C4⋊C4448(C7xC4:C4).3C4448,134
(C7×C4⋊C4).4C4 = C7×C4.10D8φ: C4/C1 → C4 ⊆ Out C7×C4⋊C4448(C7xC4:C4).4C4448,136
(C7×C4⋊C4).5C4 = C28.57D8φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).5C4448,91
(C7×C4⋊C4).6C4 = C28.26Q16φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4).6C4448,92
(C7×C4⋊C4).7C4 = C28.5C42φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).7C4448,531
(C7×C4⋊C4).8C4 = C42.43D14φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).8C4448,533
(C7×C4⋊C4).9C4 = C42.187D14φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).9C4448,534
(C7×C4⋊C4).10C4 = D4×C7⋊C8φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).10C4448,544
(C7×C4⋊C4).11C4 = C42.47D14φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).11C4448,545
(C7×C4⋊C4).12C4 = C28⋊3M4(2)φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).12C4448,546
(C7×C4⋊C4).13C4 = Q8×C7⋊C8φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4).13C4448,557
(C7×C4⋊C4).14C4 = C42.210D14φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4).14C4448,558
(C7×C4⋊C4).15C4 = C7×D4⋊C8φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).15C4448,129
(C7×C4⋊C4).16C4 = C7×Q8⋊C8φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4).16C4448,130
(C7×C4⋊C4).17C4 = C7×C42.6C22φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).17C4448,832
(C7×C4⋊C4).18C4 = C7×C42.7C22φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).18C4448,841
(C7×C4⋊C4).19C4 = C7×C8⋊9D4φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).19C4448,843
(C7×C4⋊C4).20C4 = C7×C8⋊6D4φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4224(C7xC4:C4).20C4448,844
(C7×C4⋊C4).21C4 = C7×C8⋊4Q8φ: C4/C2 → C2 ⊆ Out C7×C4⋊C4448(C7xC4:C4).21C4448,854
(C7×C4⋊C4).22C4 = C7×C8○2M4(2)φ: trivial image224(C7xC4:C4).22C4448,813
(C7×C4⋊C4).23C4 = D4×C56φ: trivial image224(C7xC4:C4).23C4448,842
(C7×C4⋊C4).24C4 = Q8×C56φ: trivial image448(C7xC4:C4).24C4448,853

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