# Extensions 1→N→G→Q→1 with N=C42 and Q=C6

Direct product G=N×Q with N=C42 and Q=C6
dρLabelID
C2×C4×C1296C2xC4xC1296,161

Semidirect products G=N:Q with N=C42 and Q=C6
extensionφ:Q→Aut NdρLabelID
C421C6 = C42⋊C6φ: C6/C1C6 ⊆ Aut C42166C4^2:1C696,71
C422C6 = C23.A4φ: C6/C1C6 ⊆ Aut C42126+C4^2:2C696,72
C423C6 = C2×C42⋊C3φ: C6/C2C3 ⊆ Aut C42123C4^2:3C696,68
C424C6 = C3×C42⋊C2φ: C6/C3C2 ⊆ Aut C4248C4^2:4C696,164
C425C6 = C3×C422C2φ: C6/C3C2 ⊆ Aut C4248C4^2:5C696,173
C426C6 = C3×C4≀C2φ: C6/C3C2 ⊆ Aut C42242C4^2:6C696,54
C427C6 = D4×C12φ: C6/C3C2 ⊆ Aut C4248C4^2:7C696,165
C428C6 = C3×C4.4D4φ: C6/C3C2 ⊆ Aut C4248C4^2:8C696,171
C429C6 = C3×C41D4φ: C6/C3C2 ⊆ Aut C4248C4^2:9C696,174

Non-split extensions G=N.Q with N=C42 and Q=C6
extensionφ:Q→Aut NdρLabelID
C42.1C6 = C3×C8⋊C4φ: C6/C3C2 ⊆ Aut C4296C4^2.1C696,47
C42.2C6 = C3×C4⋊C8φ: C6/C3C2 ⊆ Aut C4296C4^2.2C696,55
C42.3C6 = Q8×C12φ: C6/C3C2 ⊆ Aut C4296C4^2.3C696,166
C42.4C6 = C3×C42.C2φ: C6/C3C2 ⊆ Aut C4296C4^2.4C696,172
C42.5C6 = C3×C4⋊Q8φ: C6/C3C2 ⊆ Aut C4296C4^2.5C696,175

׿
×
𝔽