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Extensions 1→N→G→Q→1 with N=C34 and Q=C2×C4

Direct product G=N×Q with N=C34 and Q=C2×C4
dρLabelID
C22×C68272C2^2xC68272,46

Semidirect products G=N:Q with N=C34 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C34⋊(C2×C4) = C22×C17⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C3468C34:(C2xC4)272,52
C34⋊2(C2×C4) = C2×C4×D17φ: C2×C4/C4 → C2 ⊆ Aut C34136C34:2(C2xC4)272,37
C34⋊3(C2×C4) = C22×Dic17φ: C2×C4/C22 → C2 ⊆ Aut C34272C34:3(C2xC4)272,44

Non-split extensions G=N.Q with N=C34 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C34.1(C2×C4) = C68.C4φ: C2×C4/C2 → C4 ⊆ Aut C341364C34.1(C2xC4)272,29
C34.2(C2×C4) = D34.4C4φ: C2×C4/C2 → C4 ⊆ Aut C341364C34.2(C2xC4)272,30
C34.3(C2×C4) = C4×C17⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C34684C34.3(C2xC4)272,31
C34.4(C2×C4) = C68⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C34684C34.4(C2xC4)272,32
C34.5(C2×C4) = C2×C17⋊2C8φ: C2×C4/C2 → C4 ⊆ Aut C34272C34.5(C2xC4)272,33
C34.6(C2×C4) = C17⋊M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C341364-C34.6(C2xC4)272,34
C34.7(C2×C4) = D17.D4φ: C2×C4/C2 → C4 ⊆ Aut C34684+C34.7(C2xC4)272,35
C34.8(C2×C4) = C8×D17φ: C2×C4/C4 → C2 ⊆ Aut C341362C34.8(C2xC4)272,4
C34.9(C2×C4) = C8⋊D17φ: C2×C4/C4 → C2 ⊆ Aut C341362C34.9(C2xC4)272,5
C34.10(C2×C4) = C4×Dic17φ: C2×C4/C4 → C2 ⊆ Aut C34272C34.10(C2xC4)272,11
C34.11(C2×C4) = C34.D4φ: C2×C4/C4 → C2 ⊆ Aut C34272C34.11(C2xC4)272,12
C34.12(C2×C4) = D34⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C34136C34.12(C2xC4)272,14
C34.13(C2×C4) = C2×C17⋊3C8φ: C2×C4/C22 → C2 ⊆ Aut C34272C34.13(C2xC4)272,9
C34.14(C2×C4) = C68.4C4φ: C2×C4/C22 → C2 ⊆ Aut C341362C34.14(C2xC4)272,10
C34.15(C2×C4) = C68⋊3C4φ: C2×C4/C22 → C2 ⊆ Aut C34272C34.15(C2xC4)272,13
C34.16(C2×C4) = C23.D17φ: C2×C4/C22 → C2 ⊆ Aut C34136C34.16(C2xC4)272,19
C34.17(C2×C4) = C22⋊C4×C17central extension (φ=1)136C34.17(C2xC4)272,21
C34.18(C2×C4) = C4⋊C4×C17central extension (φ=1)272C34.18(C2xC4)272,22
C34.19(C2×C4) = M4(2)×C17central extension (φ=1)1362C34.19(C2xC4)272,24

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