# Extensions 1→N→G→Q→1 with N=C7×C23⋊C4 and Q=C2

Direct product G=N×Q with N=C7×C23⋊C4 and Q=C2
dρLabelID
C14×C23⋊C4112C14xC2^3:C4448,817

Semidirect products G=N:Q with N=C7×C23⋊C4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C7×C23⋊C4)⋊1C2 = C7⋊C2≀C4φ: C2/C1C2 ⊆ Out C7×C23⋊C4568+(C7xC2^3:C4):1C2448,28
(C7×C23⋊C4)⋊2C2 = C23.2D28φ: C2/C1C2 ⊆ Out C7×C23⋊C4568+(C7xC2^3:C4):2C2448,31
(C7×C23⋊C4)⋊3C2 = C23⋊C45D7φ: C2/C1C2 ⊆ Out C7×C23⋊C41128-(C7xC2^3:C4):3C2448,274
(C7×C23⋊C4)⋊4C2 = C23⋊D28φ: C2/C1C2 ⊆ Out C7×C23⋊C4568+(C7xC2^3:C4):4C2448,275
(C7×C23⋊C4)⋊5C2 = C23.5D28φ: C2/C1C2 ⊆ Out C7×C23⋊C41128-(C7xC2^3:C4):5C2448,276
(C7×C23⋊C4)⋊6C2 = D7×C23⋊C4φ: C2/C1C2 ⊆ Out C7×C23⋊C4568+(C7xC2^3:C4):6C2448,277
(C7×C23⋊C4)⋊7C2 = C7×C2≀C4φ: C2/C1C2 ⊆ Out C7×C23⋊C4564(C7xC2^3:C4):7C2448,155
(C7×C23⋊C4)⋊8C2 = C7×C42⋊C4φ: C2/C1C2 ⊆ Out C7×C23⋊C4564(C7xC2^3:C4):8C2448,157
(C7×C23⋊C4)⋊9C2 = C7×C2≀C22φ: C2/C1C2 ⊆ Out C7×C23⋊C4564(C7xC2^3:C4):9C2448,865
(C7×C23⋊C4)⋊10C2 = C7×C23.7D4φ: C2/C1C2 ⊆ Out C7×C23⋊C41124(C7xC2^3:C4):10C2448,866
(C7×C23⋊C4)⋊11C2 = C7×C23.C23φ: trivial image1124(C7xC2^3:C4):11C2448,818

Non-split extensions G=N.Q with N=C7×C23⋊C4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C7×C23⋊C4).1C2 = (C2×C28).D4φ: C2/C1C2 ⊆ Out C7×C23⋊C41128-(C7xC2^3:C4).1C2448,29
(C7×C23⋊C4).2C2 = C23.D28φ: C2/C1C2 ⊆ Out C7×C23⋊C41128-(C7xC2^3:C4).2C2448,30
(C7×C23⋊C4).3C2 = C7×C23.D4φ: C2/C1C2 ⊆ Out C7×C23⋊C41124(C7xC2^3:C4).3C2448,156
(C7×C23⋊C4).4C2 = C7×C423C4φ: C2/C1C2 ⊆ Out C7×C23⋊C41124(C7xC2^3:C4).4C2448,158

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