# Extensions 1→N→G→Q→1 with N=C23 and Q=C7×D4

Direct product G=N×Q with N=C23 and Q=C7×D4
dρLabelID
D4×C22×C14224D4xC2^2xC14448,1386

Semidirect products G=N:Q with N=C23 and Q=C7×D4
extensionφ:Q→Aut NdρLabelID
C23⋊(C7×D4) = C7×C2≀C22φ: C7×D4/C7D4 ⊆ Aut C23564C2^3:(C7xD4)448,865
C232(C7×D4) = D4×F8φ: C7×D4/D4C7 ⊆ Aut C232814+C2^3:2(C7xD4)448,1363
C233(C7×D4) = C7×C232D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3:3(C7xD4)448,800
C234(C7×D4) = C7×C233D4φ: C7×D4/C14C22 ⊆ Aut C23112C2^3:4(C7xD4)448,1317
C235(C7×D4) = C14×C4⋊D4φ: C7×D4/C28C2 ⊆ Aut C23224C2^3:5(C7xD4)448,1305
C236(C7×D4) = C14×C22≀C2φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3:6(C7xD4)448,1304

Non-split extensions G=N.Q with N=C23 and Q=C7×D4
extensionφ:Q→Aut NdρLabelID
C23.1(C7×D4) = C7×C2≀C4φ: C7×D4/C7D4 ⊆ Aut C23564C2^3.1(C7xD4)448,155
C23.2(C7×D4) = C7×C23.D4φ: C7×D4/C7D4 ⊆ Aut C231124C2^3.2(C7xD4)448,156
C23.3(C7×D4) = C7×C42⋊C4φ: C7×D4/C7D4 ⊆ Aut C23564C2^3.3(C7xD4)448,157
C23.4(C7×D4) = C7×C423C4φ: C7×D4/C7D4 ⊆ Aut C231124C2^3.4(C7xD4)448,158
C23.5(C7×D4) = C7×D44D4φ: C7×D4/C7D4 ⊆ Aut C23564C2^3.5(C7xD4)448,861
C23.6(C7×D4) = C7×D4.9D4φ: C7×D4/C7D4 ⊆ Aut C231124C2^3.6(C7xD4)448,863
C23.7(C7×D4) = C7×C23.7D4φ: C7×D4/C7D4 ⊆ Aut C231124C2^3.7(C7xD4)448,866
C23.8(C7×D4) = C7×C4.9C42φ: C7×D4/C14C22 ⊆ Aut C231124C2^3.8(C7xD4)448,141
C23.9(C7×D4) = C7×C23.10D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3.9(C7xD4)448,802
C23.10(C7×D4) = C7×C23.11D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3.10(C7xD4)448,805
C23.11(C7×D4) = C14×C23⋊C4φ: C7×D4/C14C22 ⊆ Aut C23112C2^3.11(C7xD4)448,817
C23.12(C7×D4) = C7×C42⋊C22φ: C7×D4/C14C22 ⊆ Aut C231124C2^3.12(C7xD4)448,829
C23.13(C7×D4) = C7×D4⋊D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3.13(C7xD4)448,857
C23.14(C7×D4) = C7×D4.7D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3.14(C7xD4)448,860
C23.15(C7×D4) = C7×C8⋊D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3.15(C7xD4)448,876
C23.16(C7×D4) = C7×C82D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3.16(C7xD4)448,877
C23.17(C7×D4) = C7×C8.D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3.17(C7xD4)448,878
C23.18(C7×D4) = C7×C23.19D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3.18(C7xD4)448,890
C23.19(C7×D4) = C7×C23.20D4φ: C7×D4/C14C22 ⊆ Aut C23224C2^3.19(C7xD4)448,893
C23.20(C7×D4) = C7×D8⋊C22φ: C7×D4/C14C22 ⊆ Aut C231124C2^3.20(C7xD4)448,1358
C23.21(C7×D4) = C7×C23.7Q8φ: C7×D4/C28C2 ⊆ Aut C23224C2^3.21(C7xD4)448,788
C23.22(C7×D4) = C7×C23.23D4φ: C7×D4/C28C2 ⊆ Aut C23224C2^3.22(C7xD4)448,794
C23.23(C7×D4) = C7×C23.24D4φ: C7×D4/C28C2 ⊆ Aut C23224C2^3.23(C7xD4)448,824
C23.24(C7×D4) = C7×C23.25D4φ: C7×D4/C28C2 ⊆ Aut C23224C2^3.24(C7xD4)448,835
C23.25(C7×D4) = C7×C88D4φ: C7×D4/C28C2 ⊆ Aut C23224C2^3.25(C7xD4)448,873
C23.26(C7×D4) = C7×C87D4φ: C7×D4/C28C2 ⊆ Aut C23224C2^3.26(C7xD4)448,874
C23.27(C7×D4) = C7×C8.18D4φ: C7×D4/C28C2 ⊆ Aut C23224C2^3.27(C7xD4)448,875
C23.28(C7×D4) = C14×C4○D8φ: C7×D4/C28C2 ⊆ Aut C23224C2^3.28(C7xD4)448,1355
C23.29(C7×D4) = C7×C22.SD16φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.29(C7xD4)448,131
C23.30(C7×D4) = C7×C23.31D4φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.30(C7xD4)448,132
C23.31(C7×D4) = C7×C426C4φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.31(C7xD4)448,143
C23.32(C7×D4) = C7×C23.9D4φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.32(C7xD4)448,146
C23.33(C7×D4) = C7×C243C4φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.33(C7xD4)448,787
C23.34(C7×D4) = C7×C23.34D4φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.34(C7xD4)448,789
C23.35(C7×D4) = C7×C23.8Q8φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.35(C7xD4)448,793
C23.36(C7×D4) = C7×C23.36D4φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.36(C7xD4)448,825
C23.37(C7×D4) = C7×C23.37D4φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.37(C7xD4)448,826
C23.38(C7×D4) = C7×C23.38D4φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.38(C7xD4)448,827
C23.39(C7×D4) = C14×C4≀C2φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.39(C7xD4)448,828
C23.40(C7×D4) = C7×M4(2)⋊C4φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.40(C7xD4)448,836
C23.41(C7×D4) = C7×C22⋊D8φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.41(C7xD4)448,855
C23.42(C7×D4) = C7×Q8⋊D4φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.42(C7xD4)448,856
C23.43(C7×D4) = C7×C22⋊SD16φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.43(C7xD4)448,858
C23.44(C7×D4) = C7×C22⋊Q16φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.44(C7xD4)448,859
C23.45(C7×D4) = C7×C22.D8φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.45(C7xD4)448,888
C23.46(C7×D4) = C7×C23.46D4φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.46(C7xD4)448,889
C23.47(C7×D4) = C7×C23.47D4φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.47(C7xD4)448,891
C23.48(C7×D4) = C7×C23.48D4φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.48(C7xD4)448,892
C23.49(C7×D4) = C14×C22.D4φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.49(C7xD4)448,1307
C23.50(C7×D4) = C14×C8⋊C22φ: C7×D4/C2×C14C2 ⊆ Aut C23112C2^3.50(C7xD4)448,1356
C23.51(C7×D4) = C14×C8.C22φ: C7×D4/C2×C14C2 ⊆ Aut C23224C2^3.51(C7xD4)448,1357
C23.52(C7×D4) = C7×C22.4Q16central extension (φ=1)448C2^3.52(C7xD4)448,144
C23.53(C7×D4) = C14×C2.C42central extension (φ=1)448C2^3.53(C7xD4)448,783
C23.54(C7×D4) = C14×D4⋊C4central extension (φ=1)224C2^3.54(C7xD4)448,822
C23.55(C7×D4) = C14×Q8⋊C4central extension (φ=1)448C2^3.55(C7xD4)448,823
C23.56(C7×D4) = C14×C4.Q8central extension (φ=1)448C2^3.56(C7xD4)448,833
C23.57(C7×D4) = C14×C2.D8central extension (φ=1)448C2^3.57(C7xD4)448,834
C23.58(C7×D4) = C22⋊C4×C2×C14central extension (φ=1)224C2^3.58(C7xD4)448,1295
C23.59(C7×D4) = C4⋊C4×C2×C14central extension (φ=1)448C2^3.59(C7xD4)448,1296
C23.60(C7×D4) = D8×C2×C14central extension (φ=1)224C2^3.60(C7xD4)448,1352
C23.61(C7×D4) = SD16×C2×C14central extension (φ=1)224C2^3.61(C7xD4)448,1353
C23.62(C7×D4) = Q16×C2×C14central extension (φ=1)448C2^3.62(C7xD4)448,1354

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