# Extensions 1→N→G→Q→1 with N=C42.C2 and Q=C2

Direct product G=N×Q with N=C42.C2 and Q=C2
dρLabelID
C2×C42.C264C2xC4^2.C264,208

Semidirect products G=N:Q with N=C42.C2 and Q=C2
extensionφ:Q→Out NdρLabelID
C42.C21C2 = D4.Q8φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:1C264,159
C42.C22C2 = C42.78C22φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:2C264,169
C42.C23C2 = C42.29C22φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:3C264,171
C42.C24C2 = C22.33C24φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:4C264,220
C42.C25C2 = C22.34C24φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:5C264,221
C42.C26C2 = C22.35C24φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:6C264,222
C42.C27C2 = C23.41C23φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:7C264,225
C42.C28C2 = C22.46C24φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:8C264,233
C42.C29C2 = C22.47C24φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:9C264,234
C42.C210C2 = D43Q8φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:10C264,235
C42.C211C2 = C22.56C24φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:11C264,243
C42.C212C2 = C22.57C24φ: C2/C1C2 ⊆ Out C42.C232C4^2.C2:12C264,244
C42.C213C2 = C23.36C23φ: trivial image32C4^2.C2:13C264,210
C42.C214C2 = C23.37C23φ: trivial image32C4^2.C2:14C264,214

Non-split extensions G=N.Q with N=C42.C2 and Q=C2
extensionφ:Q→Out NdρLabelID
C42.C2.1C2 = C42.2C22φ: C2/C1C2 ⊆ Out C42.C264C4^2.C2.1C264,11
C42.C2.2C2 = Q8.Q8φ: C2/C1C2 ⊆ Out C42.C264C4^2.C2.2C264,160
C42.C2.3C2 = C42.30C22φ: C2/C1C2 ⊆ Out C42.C264C4^2.C2.3C264,172
C42.C2.4C2 = C8.5Q8φ: C2/C1C2 ⊆ Out C42.C264C4^2.C2.4C264,180
C42.C2.5C2 = C8⋊Q8φ: C2/C1C2 ⊆ Out C42.C264C4^2.C2.5C264,182
C42.C2.6C2 = Q83Q8φ: C2/C1C2 ⊆ Out C42.C264C4^2.C2.6C264,238
C42.C2.7C2 = C22.58C24φ: C2/C1C2 ⊆ Out C42.C264C4^2.C2.7C264,245

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