# Extensions 1→N→G→Q→1 with N=C22 and Q=C7×M4(2)

Direct product G=N×Q with N=C22 and Q=C7×M4(2)
dρLabelID
M4(2)×C2×C14224M4(2)xC2xC14448,1349

Semidirect products G=N:Q with N=C22 and Q=C7×M4(2)
extensionφ:Q→Aut NdρLabelID
C221(C7×M4(2)) = C7×C89D4φ: C7×M4(2)/C56C2 ⊆ Aut C22224C2^2:1(C7xM4(2))448,843
C222(C7×M4(2)) = C7×C24.4C4φ: C7×M4(2)/C2×C28C2 ⊆ Aut C22112C2^2:2(C7xM4(2))448,815

Non-split extensions G=N.Q with N=C22 and Q=C7×M4(2)
extensionφ:Q→Aut NdρLabelID
C22.1(C7×M4(2)) = C7×D4.C8φ: C7×M4(2)/C56C2 ⊆ Aut C222242C2^2.1(C7xM4(2))448,154
C22.2(C7×M4(2)) = C7×C23⋊C8φ: C7×M4(2)/C2×C28C2 ⊆ Aut C22112C2^2.2(C7xM4(2))448,127
C22.3(C7×M4(2)) = C7×C22.M4(2)φ: C7×M4(2)/C2×C28C2 ⊆ Aut C22224C2^2.3(C7xM4(2))448,128
C22.4(C7×M4(2)) = C7×C16⋊C4φ: C7×M4(2)/C2×C28C2 ⊆ Aut C221124C2^2.4(C7xM4(2))448,151
C22.5(C7×M4(2)) = C7×C8.C8φ: C7×M4(2)/C2×C28C2 ⊆ Aut C221122C2^2.5(C7xM4(2))448,168
C22.6(C7×M4(2)) = C7×C42.6C4φ: C7×M4(2)/C2×C28C2 ⊆ Aut C22224C2^2.6(C7xM4(2))448,840
C22.7(C7×M4(2)) = C7×C22.7C42central extension (φ=1)448C2^2.7(C7xM4(2))448,140
C22.8(C7×M4(2)) = C14×C8⋊C4central extension (φ=1)448C2^2.8(C7xM4(2))448,811
C22.9(C7×M4(2)) = C14×C22⋊C8central extension (φ=1)224C2^2.9(C7xM4(2))448,814
C22.10(C7×M4(2)) = C14×C4⋊C8central extension (φ=1)448C2^2.10(C7xM4(2))448,830

׿
×
𝔽