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Extensions 1→N→G→Q→1 with N=C34 and Q=C23

Direct product G=N×Q with N=C34 and Q=C23
dρLabelID
C23×C34272C2^3xC34272,54

Semidirect products G=N:Q with N=C34 and Q=C23
extensionφ:Q→Aut NdρLabelID
C34⋊C23 = C23×D17φ: C23/C22 → C2 ⊆ Aut C34136C34:C2^3272,53

Non-split extensions G=N.Q with N=C34 and Q=C23
extensionφ:Q→Aut NdρLabelID
C34.1C23 = C2×Dic34φ: C23/C22 → C2 ⊆ Aut C34272C34.1C2^3272,36
C34.2C23 = C2×C4×D17φ: C23/C22 → C2 ⊆ Aut C34136C34.2C2^3272,37
C34.3C23 = C2×D68φ: C23/C22 → C2 ⊆ Aut C34136C34.3C2^3272,38
C34.4C23 = D68⋊5C2φ: C23/C22 → C2 ⊆ Aut C341362C34.4C2^3272,39
C34.5C23 = D4×D17φ: C23/C22 → C2 ⊆ Aut C34684+C34.5C2^3272,40
C34.6C23 = D4⋊2D17φ: C23/C22 → C2 ⊆ Aut C341364-C34.6C2^3272,41
C34.7C23 = Q8×D17φ: C23/C22 → C2 ⊆ Aut C341364-C34.7C2^3272,42
C34.8C23 = D68⋊C2φ: C23/C22 → C2 ⊆ Aut C341364+C34.8C2^3272,43
C34.9C23 = C22×Dic17φ: C23/C22 → C2 ⊆ Aut C34272C34.9C2^3272,44
C34.10C23 = C2×C17⋊D4φ: C23/C22 → C2 ⊆ Aut C34136C34.10C2^3272,45
C34.11C23 = D4×C34central extension (φ=1)136C34.11C2^3272,47
C34.12C23 = Q8×C34central extension (φ=1)272C34.12C2^3272,48
C34.13C23 = C4○D4×C17central extension (φ=1)1362C34.13C2^3272,49

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