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Extensions 1→N→G→Q→1 with N=C2×C34 and Q=C22

Direct product G=N×Q with N=C2×C34 and Q=C22
dρLabelID
C23×C34272C2^3xC34272,54

Semidirect products G=N:Q with N=C2×C34 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C2×C34)⋊C22 = D4×D17φ: C22/C1 → C22 ⊆ Aut C2×C34684+(C2xC34):C2^2272,40
(C2×C34)⋊2C22 = D4×C34φ: C22/C2 → C2 ⊆ Aut C2×C34136(C2xC34):2C2^2272,47
(C2×C34)⋊3C22 = C2×C17⋊D4φ: C22/C2 → C2 ⊆ Aut C2×C34136(C2xC34):3C2^2272,45
(C2×C34)⋊4C22 = C23×D17φ: C22/C2 → C2 ⊆ Aut C2×C34136(C2xC34):4C2^2272,53

Non-split extensions G=N.Q with N=C2×C34 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C2×C34).C22 = D4⋊2D17φ: C22/C1 → C22 ⊆ Aut C2×C341364-(C2xC34).C2^2272,41
(C2×C34).2C22 = C4○D4×C17φ: C22/C2 → C2 ⊆ Aut C2×C341362(C2xC34).2C2^2272,49
(C2×C34).3C22 = C4×Dic17φ: C22/C2 → C2 ⊆ Aut C2×C34272(C2xC34).3C2^2272,11
(C2×C34).4C22 = C34.D4φ: C22/C2 → C2 ⊆ Aut C2×C34272(C2xC34).4C2^2272,12
(C2×C34).5C22 = C68⋊3C4φ: C22/C2 → C2 ⊆ Aut C2×C34272(C2xC34).5C2^2272,13
(C2×C34).6C22 = D34⋊C4φ: C22/C2 → C2 ⊆ Aut C2×C34136(C2xC34).6C2^2272,14
(C2×C34).7C22 = C23.D17φ: C22/C2 → C2 ⊆ Aut C2×C34136(C2xC34).7C2^2272,19
(C2×C34).8C22 = C2×Dic34φ: C22/C2 → C2 ⊆ Aut C2×C34272(C2xC34).8C2^2272,36
(C2×C34).9C22 = C2×C4×D17φ: C22/C2 → C2 ⊆ Aut C2×C34136(C2xC34).9C2^2272,37
(C2×C34).10C22 = C2×D68φ: C22/C2 → C2 ⊆ Aut C2×C34136(C2xC34).10C2^2272,38
(C2×C34).11C22 = D68⋊5C2φ: C22/C2 → C2 ⊆ Aut C2×C341362(C2xC34).11C2^2272,39
(C2×C34).12C22 = C22×Dic17φ: C22/C2 → C2 ⊆ Aut C2×C34272(C2xC34).12C2^2272,44
(C2×C34).13C22 = C22⋊C4×C17central extension (φ=1)136(C2xC34).13C2^2272,21
(C2×C34).14C22 = C4⋊C4×C17central extension (φ=1)272(C2xC34).14C2^2272,22
(C2×C34).15C22 = Q8×C34central extension (φ=1)272(C2xC34).15C2^2272,48

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