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Extensions 1→N→G→Q→1 with N=C2×C14 and Q=M4(2)

Direct product G=N×Q with N=C2×C14 and Q=M4(2)
dρLabelID
M4(2)×C2×C14224M4(2)xC2xC14448,1349

Semidirect products G=N:Q with N=C2×C14 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
(C2×C14)⋊1M4(2) = D14⋊M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2×C14112(C2xC14):1M4(2)448,260
(C2×C14)⋊2M4(2) = C7⋊C8⋊26D4φ: M4(2)/C4 → C22 ⊆ Aut C2×C14224(C2xC14):2M4(2)448,264
(C2×C14)⋊3M4(2) = C42.47D14φ: M4(2)/C4 → C22 ⊆ Aut C2×C14224(C2xC14):3M4(2)448,545
(C2×C14)⋊4M4(2) = C7×C8⋊9D4φ: M4(2)/C8 → C2 ⊆ Aut C2×C14224(C2xC14):4M4(2)448,843
(C2×C14)⋊5M4(2) = C56⋊32D4φ: M4(2)/C8 → C2 ⊆ Aut C2×C14224(C2xC14):5M4(2)448,645
(C2×C14)⋊6M4(2) = C22×C8⋊D7φ: M4(2)/C8 → C2 ⊆ Aut C2×C14224(C2xC14):6M4(2)448,1190
(C2×C14)⋊7M4(2) = C7×C24.4C4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14112(C2xC14):7M4(2)448,815
(C2×C14)⋊8M4(2) = C24.4Dic7φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14112(C2xC14):8M4(2)448,741
(C2×C14)⋊9M4(2) = C22×C4.Dic7φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14224(C2xC14):9M4(2)448,1234

Non-split extensions G=N.Q with N=C2×C14 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
(C2×C14).1M4(2) = (C22×D7)⋊C8φ: M4(2)/C4 → C22 ⊆ Aut C2×C14112(C2xC14).1M4(2)448,25
(C2×C14).2M4(2) = (C2×Dic7)⋊C8φ: M4(2)/C4 → C22 ⊆ Aut C2×C14224(C2xC14).2M4(2)448,26
(C2×C14).3M4(2) = C56.9Q8φ: M4(2)/C4 → C22 ⊆ Aut C2×C141124(C2xC14).3M4(2)448,68
(C2×C14).4M4(2) = C112⋊C4φ: M4(2)/C4 → C22 ⊆ Aut C2×C141124(C2xC14).4M4(2)448,69
(C2×C14).5M4(2) = Dic14.C8φ: M4(2)/C4 → C22 ⊆ Aut C2×C142244(C2xC14).5M4(2)448,72
(C2×C14).6M4(2) = C56.92D4φ: M4(2)/C4 → C22 ⊆ Aut C2×C142244(C2xC14).6M4(2)448,118
(C2×C14).7M4(2) = Dic7.M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2×C14224(C2xC14).7M4(2)448,253
(C2×C14).8M4(2) = C7×D4.C8φ: M4(2)/C8 → C2 ⊆ Aut C2×C142242(C2xC14).8M4(2)448,154
(C2×C14).9M4(2) = D28.C8φ: M4(2)/C8 → C2 ⊆ Aut C2×C142242(C2xC14).9M4(2)448,65
(C2×C14).10M4(2) = (C2×C56)⋊5C4φ: M4(2)/C8 → C2 ⊆ Aut C2×C14448(C2xC14).10M4(2)448,107
(C2×C14).11M4(2) = C2×Dic7⋊C8φ: M4(2)/C8 → C2 ⊆ Aut C2×C14448(C2xC14).11M4(2)448,633
(C2×C14).12M4(2) = C2×C56⋊C4φ: M4(2)/C8 → C2 ⊆ Aut C2×C14448(C2xC14).12M4(2)448,634
(C2×C14).13M4(2) = C2×D14⋊C8φ: M4(2)/C8 → C2 ⊆ Aut C2×C14224(C2xC14).13M4(2)448,642
(C2×C14).14M4(2) = C7×C23⋊C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14112(C2xC14).14M4(2)448,127
(C2×C14).15M4(2) = C7×C22.M4(2)φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14224(C2xC14).15M4(2)448,128
(C2×C14).16M4(2) = C7×C16⋊C4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C141124(C2xC14).16M4(2)448,151
(C2×C14).17M4(2) = C7×C8.C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C141122(C2xC14).17M4(2)448,168
(C2×C14).18M4(2) = C7×C42.6C4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14224(C2xC14).18M4(2)448,840
(C2×C14).19M4(2) = C56.16Q8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C141122(C2xC14).19M4(2)448,20
(C2×C14).20M4(2) = C28.15C42φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C141124(C2xC14).20M4(2)448,23
(C2×C14).21M4(2) = (C2×C28)⋊3C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14448(C2xC14).21M4(2)448,81
(C2×C14).22M4(2) = C24.Dic7φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14112(C2xC14).22M4(2)448,82
(C2×C14).23M4(2) = (C2×C28)⋊C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14224(C2xC14).23M4(2)448,85
(C2×C14).24M4(2) = C2×C42.D7φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14448(C2xC14).24M4(2)448,455
(C2×C14).25M4(2) = C2×C28⋊C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14448(C2xC14).25M4(2)448,457
(C2×C14).26M4(2) = C42.7Dic7φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14224(C2xC14).26M4(2)448,460
(C2×C14).27M4(2) = C2×C28.55D4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C14224(C2xC14).27M4(2)448,740
(C2×C14).28M4(2) = C7×C22.7C42central extension (φ=1)448(C2xC14).28M4(2)448,140
(C2×C14).29M4(2) = C14×C8⋊C4central extension (φ=1)448(C2xC14).29M4(2)448,811
(C2×C14).30M4(2) = C14×C22⋊C8central extension (φ=1)224(C2xC14).30M4(2)448,814
(C2×C14).31M4(2) = C14×C4⋊C8central extension (φ=1)448(C2xC14).31M4(2)448,830

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