# Extensions 1→N→G→Q→1 with N=C2×M4(2) and Q=D7

Direct product G=N×Q with N=C2×M4(2) and Q=D7
dρLabelID
C2×D7×M4(2)112C2xD7xM4(2)448,1196

Semidirect products G=N:Q with N=C2×M4(2) and Q=D7
extensionφ:Q→Out NdρLabelID
(C2×M4(2))⋊1D7 = C562D4φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)):1D7448,668
(C2×M4(2))⋊2D7 = C563D4φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)):2D7448,669
(C2×M4(2))⋊3D7 = C2×C8⋊D14φ: D7/C7C2 ⊆ Out C2×M4(2)112(C2xM4(2)):3D7448,1199
(C2×M4(2))⋊4D7 = C2×C8.D14φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)):4D7448,1200
(C2×M4(2))⋊5D7 = C56.9C23φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)):5D7448,1201
(C2×M4(2))⋊6D7 = D146M4(2)φ: D7/C7C2 ⊆ Out C2×M4(2)112(C2xM4(2)):6D7448,660
(C2×M4(2))⋊7D7 = C56⋊D4φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)):7D7448,661
(C2×M4(2))⋊8D7 = C5618D4φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)):8D7448,662
(C2×M4(2))⋊9D7 = (C2×D28).14C4φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)):9D7448,663
(C2×M4(2))⋊10D7 = C2×C28.46D4φ: D7/C7C2 ⊆ Out C2×M4(2)112(C2xM4(2)):10D7448,664
(C2×M4(2))⋊11D7 = C23.48D28φ: D7/C7C2 ⊆ Out C2×M4(2)112(C2xM4(2)):11D7448,665
(C2×M4(2))⋊12D7 = M4(2).31D14φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)):12D7448,666
(C2×M4(2))⋊13D7 = C23.49D28φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)):13D7448,667
(C2×M4(2))⋊14D7 = C2×D284C4φ: D7/C7C2 ⊆ Out C2×M4(2)112(C2xM4(2)):14D7448,672
(C2×M4(2))⋊15D7 = C23.20D28φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)):15D7448,673
(C2×M4(2))⋊16D7 = C28.70C24φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)):16D7448,1198
(C2×M4(2))⋊17D7 = C2×D28.C4φ: trivial image224(C2xM4(2)):17D7448,1197

Non-split extensions G=N.Q with N=C2×M4(2) and Q=D7
extensionφ:Q→Out NdρLabelID
(C2×M4(2)).1D7 = C23.47D28φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)).1D7448,655
(C2×M4(2)).2D7 = M4(2).Dic7φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)).2D7448,659
(C2×M4(2)).3D7 = C56.4D4φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)).3D7448,671
(C2×M4(2)).4D7 = C56.D4φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)).4D7448,110
(C2×M4(2)).5D7 = M4(2)⋊Dic7φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)).5D7448,111
(C2×M4(2)).6D7 = C28.3C42φ: D7/C7C2 ⊆ Out C2×M4(2)112(C2xM4(2)).6D7448,112
(C2×M4(2)).7D7 = (C2×C56)⋊C4φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)).7D7448,113
(C2×M4(2)).8D7 = C23.9D28φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)).8D7448,114
(C2×M4(2)).9D7 = C28.4C42φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)).9D7448,115
(C2×M4(2)).10D7 = M4(2)⋊4Dic7φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)).10D7448,116
(C2×M4(2)).11D7 = C28.21C42φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)).11D7448,117
(C2×M4(2)).12D7 = Dic74M4(2)φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)).12D7448,652
(C2×M4(2)).13D7 = C28.439(C2×D4)φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)).13D7448,653
(C2×M4(2)).14D7 = C23.46D28φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)).14D7448,654
(C2×M4(2)).15D7 = C2×C28.53D4φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)).15D7448,657
(C2×M4(2)).16D7 = C23.Dic14φ: D7/C7C2 ⊆ Out C2×M4(2)1124(C2xM4(2)).16D7448,658
(C2×M4(2)).17D7 = C2×C4.12D28φ: D7/C7C2 ⊆ Out C2×M4(2)224(C2xM4(2)).17D7448,670
(C2×M4(2)).18D7 = M4(2)×Dic7φ: trivial image224(C2xM4(2)).18D7448,651
(C2×M4(2)).19D7 = C28.7C42φ: trivial image224(C2xM4(2)).19D7448,656

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