# Extensions 1→N→G→Q→1 with N=C7×M4(2) and Q=C4

Direct product G=N×Q with N=C7×M4(2) and Q=C4
dρLabelID
M4(2)×C28224M4(2)xC28448,812

Semidirect products G=N:Q with N=C7×M4(2) and Q=C4
extensionφ:Q→Out NdρLabelID
(C7×M4(2))⋊1C4 = C23.47D28φ: C4/C2C2 ⊆ Out C7×M4(2)224(C7xM4(2)):1C4448,655
(C7×M4(2))⋊2C4 = M4(2)×Dic7φ: C4/C2C2 ⊆ Out C7×M4(2)224(C7xM4(2)):2C4448,651
(C7×M4(2))⋊3C4 = C28.7C42φ: C4/C2C2 ⊆ Out C7×M4(2)224(C7xM4(2)):3C4448,656
(C7×M4(2))⋊4C4 = C7×M4(2)⋊C4φ: C4/C2C2 ⊆ Out C7×M4(2)224(C7xM4(2)):4C4448,836
(C7×M4(2))⋊5C4 = M4(2)⋊Dic7φ: C4/C2C2 ⊆ Out C7×M4(2)224(C7xM4(2)):5C4448,111
(C7×M4(2))⋊6C4 = C28.3C42φ: C4/C2C2 ⊆ Out C7×M4(2)112(C7xM4(2)):6C4448,112
(C7×M4(2))⋊7C4 = M4(2)⋊4Dic7φ: C4/C2C2 ⊆ Out C7×M4(2)1124(C7xM4(2)):7C4448,116
(C7×M4(2))⋊8C4 = C7×C426C4φ: C4/C2C2 ⊆ Out C7×M4(2)112(C7xM4(2)):8C4448,143
(C7×M4(2))⋊9C4 = C7×C22.C42φ: C4/C2C2 ⊆ Out C7×M4(2)224(C7xM4(2)):9C4448,147
(C7×M4(2))⋊10C4 = C7×M4(2)⋊4C4φ: C4/C2C2 ⊆ Out C7×M4(2)1124(C7xM4(2)):10C4448,148
(C7×M4(2))⋊11C4 = C7×C82M4(2)φ: trivial image224(C7xM4(2)):11C4448,813

Non-split extensions G=N.Q with N=C7×M4(2) and Q=C4
extensionφ:Q→Out NdρLabelID
(C7×M4(2)).1C4 = M4(2).Dic7φ: C4/C2C2 ⊆ Out C7×M4(2)1124(C7xM4(2)).1C4448,659
(C7×M4(2)).2C4 = C56.70C23φ: C4/C2C2 ⊆ Out C7×M4(2)2244(C7xM4(2)).2C4448,674
(C7×M4(2)).3C4 = C7×M4(2).C4φ: C4/C2C2 ⊆ Out C7×M4(2)1124(C7xM4(2)).3C4448,838
(C7×M4(2)).4C4 = C28.4C42φ: C4/C2C2 ⊆ Out C7×M4(2)224(C7xM4(2)).4C4448,115
(C7×M4(2)).5C4 = C56.92D4φ: C4/C2C2 ⊆ Out C7×M4(2)2244(C7xM4(2)).5C4448,118
(C7×M4(2)).6C4 = C7×C4.C42φ: C4/C2C2 ⊆ Out C7×M4(2)224(C7xM4(2)).6C4448,145
(C7×M4(2)).7C4 = C7×D4.C8φ: C4/C2C2 ⊆ Out C7×M4(2)2242(C7xM4(2)).7C4448,154
(C7×M4(2)).8C4 = C7×D4○C16φ: trivial image2242(C7xM4(2)).8C4448,912

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