# Extensions 1→N→G→Q→1 with N=C4○D12 and Q=C6

Direct product G=N×Q with N=C4○D12 and Q=C6
dρLabelID
C6×C4○D1248C6xC4oD12288,991

Semidirect products G=N:Q with N=C4○D12 and Q=C6
extensionφ:Q→Out NdρLabelID
C4○D121C6 = C3×C4○D24φ: C6/C3C2 ⊆ Out C4○D12482C4oD12:1C6288,675
C4○D122C6 = C3×C8⋊D6φ: C6/C3C2 ⊆ Out C4○D12484C4oD12:2C6288,679
C4○D123C6 = C3×D126C22φ: C6/C3C2 ⊆ Out C4○D12244C4oD12:3C6288,703
C4○D124C6 = C3×Q8.13D6φ: C6/C3C2 ⊆ Out C4○D12484C4oD12:4C6288,721
C4○D125C6 = C3×D46D6φ: C6/C3C2 ⊆ Out C4○D12244C4oD12:5C6288,994
C4○D126C6 = C3×Q8.15D6φ: C6/C3C2 ⊆ Out C4○D12484C4oD12:6C6288,997
C4○D127C6 = C3×S3×C4○D4φ: C6/C3C2 ⊆ Out C4○D12484C4oD12:7C6288,998
C4○D128C6 = C3×D4○D12φ: C6/C3C2 ⊆ Out C4○D12484C4oD12:8C6288,999
C4○D129C6 = C3×Q8○D12φ: C6/C3C2 ⊆ Out C4○D12484C4oD12:9C6288,1000

Non-split extensions G=N.Q with N=C4○D12 and Q=C6
extensionφ:Q→Out NdρLabelID
C4○D12.1C6 = C3×C424S3φ: C6/C3C2 ⊆ Out C4○D12242C4oD12.1C6288,239
C4○D12.2C6 = C3×D12⋊C4φ: C6/C3C2 ⊆ Out C4○D12484C4oD12.2C6288,259
C4○D12.3C6 = C3×D12.C4φ: C6/C3C2 ⊆ Out C4○D12484C4oD12.3C6288,678
C4○D12.4C6 = C3×C8.D6φ: C6/C3C2 ⊆ Out C4○D12484C4oD12.4C6288,680
C4○D12.5C6 = C3×Q8.11D6φ: C6/C3C2 ⊆ Out C4○D12484C4oD12.5C6288,713
C4○D12.6C6 = C3×C8○D12φ: trivial image482C4oD12.6C6288,672

׿
×
𝔽