# Extensions 1→N→G→Q→1 with N=C2×2+ 1+4 and Q=C2

Direct product G=N×Q with N=C2×2+ 1+4 and Q=C2
dρLabelID
C22×2+ 1+432C2^2xES+(2,2)128,2323

Semidirect products G=N:Q with N=C2×2+ 1+4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×2+ 1+4)⋊1C2 = C4○D4⋊D4φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)):1C2128,1740
(C2×2+ 1+4)⋊2C2 = (C2×D4)⋊21D4φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)):2C2128,1744
(C2×2+ 1+4)⋊3C2 = C2×D44D4φ: C2/C1C2 ⊆ Out C2×2+ 1+416(C2xES+(2,2)):3C2128,1746
(C2×2+ 1+4)⋊4C2 = M4(2)⋊C23φ: C2/C1C2 ⊆ Out C2×2+ 1+4168+(C2xES+(2,2)):4C2128,1751
(C2×2+ 1+4)⋊5C2 = C2×C2≀C22φ: C2/C1C2 ⊆ Out C2×2+ 1+416(C2xES+(2,2)):5C2128,1755
(C2×2+ 1+4)⋊6C2 = C24⋊C23φ: C2/C1C2 ⊆ Out C2×2+ 1+4168+(C2xES+(2,2)):6C2128,1758
(C2×2+ 1+4)⋊7C2 = C22.73C25φ: C2/C1C2 ⊆ Out C2×2+ 1+416(C2xES+(2,2)):7C2128,2216
(C2×2+ 1+4)⋊8C2 = C22.74C25φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)):8C2128,2217
(C2×2+ 1+4)⋊9C2 = C22.77C25φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)):9C2128,2220
(C2×2+ 1+4)⋊10C2 = C4⋊2+ 1+4φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)):10C2128,2228
(C2×2+ 1+4)⋊11C2 = C22.87C25φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)):11C2128,2230
(C2×2+ 1+4)⋊12C2 = C22.89C25φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)):12C2128,2232
(C2×2+ 1+4)⋊13C2 = C2×D4○D8φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)):13C2128,2313
(C2×2+ 1+4)⋊14C2 = C2×D4○SD16φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)):14C2128,2314
(C2×2+ 1+4)⋊15C2 = D8⋊C23φ: C2/C1C2 ⊆ Out C2×2+ 1+4168+(C2xES+(2,2)):15C2128,2317
(C2×2+ 1+4)⋊16C2 = 2+ 1+6φ: C2/C1C2 ⊆ Out C2×2+ 1+4168+(C2xES+(2,2)):16C2128,2326
(C2×2+ 1+4)⋊17C2 = C2×C2.C25φ: trivial image32(C2xES+(2,2)):17C2128,2325

Non-split extensions G=N.Q with N=C2×2+ 1+4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×2+ 1+4).1C2 = 2+ 1+42C4φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)).1C2128,522
(C2×2+ 1+4).2C2 = 2+ 1+43C4φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)).2C2128,524
(C2×2+ 1+4).3C2 = C4○D4.D4φ: C2/C1C2 ⊆ Out C2×2+ 1+4168+(C2xES+(2,2)).3C2128,527
(C2×2+ 1+4).4C2 = C23.C24φ: C2/C1C2 ⊆ Out C2×2+ 1+4168+(C2xES+(2,2)).4C2128,1615
(C2×2+ 1+4).5C2 = M4(2).24C23φ: C2/C1C2 ⊆ Out C2×2+ 1+4168+(C2xES+(2,2)).5C2128,1620
(C2×2+ 1+4).6C2 = 2+ 1+45C4φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)).6C2128,1629
(C2×2+ 1+4).7C2 = D4.(C2×D4)φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)).7C2128,1741
(C2×2+ 1+4).8C2 = C2×D4.9D4φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)).8C2128,1747
(C2×2+ 1+4).9C2 = C2×C23.7D4φ: C2/C1C2 ⊆ Out C2×2+ 1+432(C2xES+(2,2)).9C2128,1756
(C2×2+ 1+4).10C2 = C4×2+ 1+4φ: trivial image32(C2xES+(2,2)).10C2128,2161

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