# Extensions 1→N→G→Q→1 with N=C23 and Q=C7×Q8

Direct product G=N×Q with N=C23 and Q=C7×Q8
dρLabelID
Q8×C22×C14448Q8xC2^2xC14448,1387

Semidirect products G=N:Q with N=C23 and Q=C7×Q8
extensionφ:Q→Aut NdρLabelID
C23⋊(C7×Q8) = Q8×F8φ: C7×Q8/Q8C7 ⊆ Aut C235614-C2^3:(C7xQ8)448,1364
C232(C7×Q8) = C7×C23⋊Q8φ: C7×Q8/C14C22 ⊆ Aut C23224C2^3:2(C7xQ8)448,801
C233(C7×Q8) = C7×C232Q8φ: C7×Q8/C14C22 ⊆ Aut C23112C2^3:3(C7xQ8)448,1326
C234(C7×Q8) = C14×C22⋊Q8φ: C7×Q8/C28C2 ⊆ Aut C23224C2^3:4(C7xQ8)448,1306

Non-split extensions G=N.Q with N=C23 and Q=C7×Q8
extensionφ:Q→Aut NdρLabelID
C23.1(C7×Q8) = C7×C4.10C42φ: C7×Q8/C14C22 ⊆ Aut C231124C2^3.1(C7xQ8)448,142
C23.2(C7×Q8) = C7×C23.9D4φ: C7×Q8/C14C22 ⊆ Aut C23112C2^3.2(C7xQ8)448,146
C23.3(C7×Q8) = C7×C23.Q8φ: C7×Q8/C14C22 ⊆ Aut C23224C2^3.3(C7xQ8)448,804
C23.4(C7×Q8) = C7×C23.4Q8φ: C7×Q8/C14C22 ⊆ Aut C23224C2^3.4(C7xQ8)448,807
C23.5(C7×Q8) = C7×M4(2).C4φ: C7×Q8/C14C22 ⊆ Aut C231124C2^3.5(C7xQ8)448,838
C23.6(C7×Q8) = C7×C4.C42φ: C7×Q8/C28C2 ⊆ Aut C23224C2^3.6(C7xQ8)448,145
C23.7(C7×Q8) = C7×C23.7Q8φ: C7×Q8/C28C2 ⊆ Aut C23224C2^3.7(C7xQ8)448,788
C23.8(C7×Q8) = C7×C23.8Q8φ: C7×Q8/C28C2 ⊆ Aut C23224C2^3.8(C7xQ8)448,793
C23.9(C7×Q8) = C14×C8.C4φ: C7×Q8/C28C2 ⊆ Aut C23224C2^3.9(C7xQ8)448,837
C23.10(C7×Q8) = C14×C2.C42central extension (φ=1)448C2^3.10(C7xQ8)448,783
C23.11(C7×Q8) = C4⋊C4×C2×C14central extension (φ=1)448C2^3.11(C7xQ8)448,1296

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