# Extensions 1→N→G→Q→1 with N=C7×C8⋊C22 and Q=C2

Direct product G=N×Q with N=C7×C8⋊C22 and Q=C2
dρLabelID
C14×C8⋊C22112C14xC8:C2^2448,1356

Semidirect products G=N:Q with N=C7×C8⋊C22 and Q=C2
extensionφ:Q→Out NdρLabelID
(C7×C8⋊C22)⋊1C2 = D7×C8⋊C22φ: C2/C1C2 ⊆ Out C7×C8⋊C22568+(C7xC8:C2^2):1C2448,1225
(C7×C8⋊C22)⋊2C2 = SD16⋊D14φ: C2/C1C2 ⊆ Out C7×C8⋊C221128-(C7xC8:C2^2):2C2448,1226
(C7×C8⋊C22)⋊3C2 = D85D14φ: C2/C1C2 ⊆ Out C7×C8⋊C221128+(C7xC8:C2^2):3C2448,1227
(C7×C8⋊C22)⋊4C2 = D86D14φ: C2/C1C2 ⊆ Out C7×C8⋊C221128-(C7xC8:C2^2):4C2448,1228
(C7×C8⋊C22)⋊5C2 = D2818D4φ: C2/C1C2 ⊆ Out C7×C8⋊C22568+(C7xC8:C2^2):5C2448,732
(C7×C8⋊C22)⋊6C2 = M4(2).D14φ: C2/C1C2 ⊆ Out C7×C8⋊C221128+(C7xC8:C2^2):6C2448,733
(C7×C8⋊C22)⋊7C2 = D28.38D4φ: C2/C1C2 ⊆ Out C7×C8⋊C221128-(C7xC8:C2^2):7C2448,735
(C7×C8⋊C22)⋊8C2 = C7×D44D4φ: C2/C1C2 ⊆ Out C7×C8⋊C22564(C7xC8:C2^2):8C2448,861
(C7×C8⋊C22)⋊9C2 = C7×D4.8D4φ: C2/C1C2 ⊆ Out C7×C8⋊C221124(C7xC8:C2^2):9C2448,862
(C7×C8⋊C22)⋊10C2 = C7×D4.4D4φ: C2/C1C2 ⊆ Out C7×C8⋊C221124(C7xC8:C2^2):10C2448,880
(C7×C8⋊C22)⋊11C2 = C7×D4○D8φ: C2/C1C2 ⊆ Out C7×C8⋊C221124(C7xC8:C2^2):11C2448,1359
(C7×C8⋊C22)⋊12C2 = C7×D4○SD16φ: C2/C1C2 ⊆ Out C7×C8⋊C221124(C7xC8:C2^2):12C2448,1360
(C7×C8⋊C22)⋊13C2 = C7×D8⋊C22φ: trivial image1124(C7xC8:C2^2):13C2448,1358

Non-split extensions G=N.Q with N=C7×C8⋊C22 and Q=C2
extensionφ:Q→Out NdρLabelID
(C7×C8⋊C22).1C2 = M4(2).13D14φ: C2/C1C2 ⊆ Out C7×C8⋊C221128-(C7xC8:C2^2).1C2448,734
(C7×C8⋊C22).2C2 = C7×D4.3D4φ: C2/C1C2 ⊆ Out C7×C8⋊C221124(C7xC8:C2^2).2C2448,879

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