Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C2×He3

Direct product G=N×Q with N=C2×C4 and Q=C2×He3
dρLabelID
C22×C4×He3144C2^2xC4xHe3432,401

Semidirect products G=N:Q with N=C2×C4 and Q=C2×He3
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×He3) = C22⋊C4×He3φ: C2×He3/He3C2 ⊆ Aut C2×C472(C2xC4):1(C2xHe3)432,204
(C2×C4)⋊2(C2×He3) = C2×D4×He3φ: C2×He3/He3C2 ⊆ Aut C2×C472(C2xC4):2(C2xHe3)432,404
(C2×C4)⋊3(C2×He3) = C4○D4×He3φ: C2×He3/He3C2 ⊆ Aut C2×C4726(C2xC4):3(C2xHe3)432,410

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×He3
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×He3) = C4⋊C4×He3φ: C2×He3/He3C2 ⊆ Aut C2×C4144(C2xC4).1(C2xHe3)432,207
(C2×C4).2(C2×He3) = M4(2)×He3φ: C2×He3/He3C2 ⊆ Aut C2×C4726(C2xC4).2(C2xHe3)432,213
(C2×C4).3(C2×He3) = C2×Q8×He3φ: C2×He3/He3C2 ⊆ Aut C2×C4144(C2xC4).3(C2xHe3)432,407
(C2×C4).4(C2×He3) = C42×He3central extension (φ=1)144(C2xC4).4(C2xHe3)432,201
(C2×C4).5(C2×He3) = C2×C8×He3central extension (φ=1)144(C2xC4).5(C2xHe3)432,210

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