# Extensions 1→N→G→Q→1 with N=C23 and Q=Q8

Direct product G=N×Q with N=C23 and Q=Q8
dρLabelID
Q8×C2364Q8xC2^364,262

Semidirect products G=N:Q with N=C23 and Q=Q8
extensionφ:Q→Aut NdρLabelID
C231Q8 = C23⋊Q8φ: Q8/C2C22 ⊆ Aut C2332C2^3:1Q864,74
C232Q8 = C232Q8φ: Q8/C2C22 ⊆ Aut C2316C2^3:2Q864,224
C233Q8 = C2×C22⋊Q8φ: Q8/C4C2 ⊆ Aut C2332C2^3:3Q864,204

Non-split extensions G=N.Q with N=C23 and Q=Q8
extensionφ:Q→Aut NdρLabelID
C23.1Q8 = C4.10C42φ: Q8/C2C22 ⊆ Aut C23164C2^3.1Q864,19
C23.2Q8 = C23.9D4φ: Q8/C2C22 ⊆ Aut C2316C2^3.2Q864,23
C23.3Q8 = C23.Q8φ: Q8/C2C22 ⊆ Aut C2332C2^3.3Q864,77
C23.4Q8 = C23.4Q8φ: Q8/C2C22 ⊆ Aut C2332C2^3.4Q864,80
C23.5Q8 = M4(2).C4φ: Q8/C2C22 ⊆ Aut C23164C2^3.5Q864,111
C23.6Q8 = C4.C42φ: Q8/C4C2 ⊆ Aut C2332C2^3.6Q864,22
C23.7Q8 = C23.7Q8φ: Q8/C4C2 ⊆ Aut C2332C2^3.7Q864,61
C23.8Q8 = C23.8Q8φ: Q8/C4C2 ⊆ Aut C2332C2^3.8Q864,66
C23.9Q8 = C2×C8.C4φ: Q8/C4C2 ⊆ Aut C2332C2^3.9Q864,110
C23.10Q8 = C2×C2.C42central extension (φ=1)64C2^3.10Q864,56
C23.11Q8 = C22×C4⋊C4central extension (φ=1)64C2^3.11Q864,194

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