# Extensions 1→N→G→Q→1 with N=C7×M5(2) and Q=C2

Direct product G=N×Q with N=C7×M5(2) and Q=C2
dρLabelID
C14×M5(2)224C14xM5(2)448,911

Semidirect products G=N:Q with N=C7×M5(2) and Q=C2
extensionφ:Q→Out NdρLabelID
(C7×M5(2))⋊1C2 = C16⋊D14φ: C2/C1C2 ⊆ Out C7×M5(2)1124+(C7xM5(2)):1C2448,442
(C7×M5(2))⋊2C2 = C16.D14φ: C2/C1C2 ⊆ Out C7×M5(2)2244-(C7xM5(2)):2C2448,443
(C7×M5(2))⋊3C2 = C7×C16⋊C22φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)):3C2448,917
(C7×M5(2))⋊4C2 = C7×Q32⋊C2φ: C2/C1C2 ⊆ Out C7×M5(2)2244(C7xM5(2)):4C2448,918
(C7×M5(2))⋊5C2 = D7×M5(2)φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)):5C2448,440
(C7×M5(2))⋊6C2 = C16.12D14φ: C2/C1C2 ⊆ Out C7×M5(2)2244(C7xM5(2)):6C2448,441
(C7×M5(2))⋊7C2 = M5(2)⋊D7φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)):7C2448,71
(C7×M5(2))⋊8C2 = Dic14.C8φ: C2/C1C2 ⊆ Out C7×M5(2)2244(C7xM5(2)):8C2448,72
(C7×M5(2))⋊9C2 = C28.3D8φ: C2/C1C2 ⊆ Out C7×M5(2)1124+(C7xM5(2)):9C2448,73
(C7×M5(2))⋊10C2 = D562C4φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)):10C2448,75
(C7×M5(2))⋊11C2 = C7×C23.C8φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)):11C2448,153
(C7×M5(2))⋊12C2 = C7×D4.C8φ: C2/C1C2 ⊆ Out C7×M5(2)2242(C7xM5(2)):12C2448,154
(C7×M5(2))⋊13C2 = C7×D82C4φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)):13C2448,164
(C7×M5(2))⋊14C2 = C7×M5(2)⋊C2φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)):14C2448,165
(C7×M5(2))⋊15C2 = C7×D4○C16φ: trivial image2242(C7xM5(2)):15C2448,912

Non-split extensions G=N.Q with N=C7×M5(2) and Q=C2
extensionφ:Q→Out NdρLabelID
(C7×M5(2)).1C2 = C16⋊Dic7φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)).1C2448,70
(C7×M5(2)).2C2 = C112⋊C4φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)).2C2448,69
(C7×M5(2)).3C2 = C7×C8.Q8φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)).3C2448,169
(C7×M5(2)).4C2 = C56.9Q8φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)).4C2448,68
(C7×M5(2)).5C2 = C28.4D8φ: C2/C1C2 ⊆ Out C7×M5(2)2244-(C7xM5(2)).5C2448,74
(C7×M5(2)).6C2 = C7×C16⋊C4φ: C2/C1C2 ⊆ Out C7×M5(2)1124(C7xM5(2)).6C2448,151
(C7×M5(2)).7C2 = C7×C8.17D4φ: C2/C1C2 ⊆ Out C7×M5(2)2244(C7xM5(2)).7C2448,166
(C7×M5(2)).8C2 = C7×C8.C8φ: C2/C1C2 ⊆ Out C7×M5(2)1122(C7xM5(2)).8C2448,168

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