# Extensions 1→N→G→Q→1 with N=D8 and Q=C23

Direct product G=N×Q with N=D8 and Q=C23
dρLabelID
C23×D864C2^3xD8128,2306

Semidirect products G=N:Q with N=D8 and Q=C23
extensionφ:Q→Out NdρLabelID
D81C23 = C22×D16φ: C23/C22C2 ⊆ Out D864D8:1C2^3128,2140
D82C23 = C2×C16⋊C22φ: C23/C22C2 ⊆ Out D832D8:2C2^3128,2144
D83C23 = C22×C8⋊C22φ: C23/C22C2 ⊆ Out D832D8:3C2^3128,2310
D84C23 = C2×D8⋊C22φ: C23/C22C2 ⊆ Out D832D8:4C2^3128,2312
D85C23 = C2×D4○SD16φ: C23/C22C2 ⊆ Out D832D8:5C2^3128,2314
D86C23 = D8⋊C23φ: C23/C22C2 ⊆ Out D8168+D8:6C2^3128,2317
D87C23 = C22×C4○D8φ: trivial image64D8:7C2^3128,2309
D88C23 = C2×D4○D8φ: trivial image32D8:8C2^3128,2313

Non-split extensions G=N.Q with N=D8 and Q=C23
extensionφ:Q→Out NdρLabelID
D8.1C23 = C22×SD32φ: C23/C22C2 ⊆ Out D864D8.1C2^3128,2141
D8.2C23 = C2×C4○D16φ: C23/C22C2 ⊆ Out D864D8.2C2^3128,2143
D8.3C23 = C2×Q32⋊C2φ: C23/C22C2 ⊆ Out D864D8.3C2^3128,2145
D8.4C23 = D16⋊C22φ: C23/C22C2 ⊆ Out D8324D8.4C2^3128,2146
D8.5C23 = D4○D16φ: C23/C22C2 ⊆ Out D8324+D8.5C2^3128,2147
D8.6C23 = D4○SD32φ: C23/C22C2 ⊆ Out D8324D8.6C2^3128,2148
D8.7C23 = Q8○D16φ: C23/C22C2 ⊆ Out D8644-D8.7C2^3128,2149
D8.8C23 = C8.C24φ: C23/C22C2 ⊆ Out D8324D8.8C2^3128,2316
D8.9C23 = C4.C25φ: C23/C22C2 ⊆ Out D8328-D8.9C2^3128,2318
D8.10C23 = C2×Q8○D8φ: trivial image64D8.10C2^3128,2315

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