# Extensions 1→N→G→Q→1 with N=C23 and Q=C4×D7

Direct product G=N×Q with N=C23 and Q=C4×D7
dρLabelID
D7×C23×C4224D7xC2^3xC4448,1366

Semidirect products G=N:Q with N=C23 and Q=C4×D7
extensionφ:Q→Aut NdρLabelID
C231(C4×D7) = D7×C23⋊C4φ: C4×D7/D7C4 ⊆ Aut C23568+C2^3:1(C4xD7)448,277
C232(C4×D7) = C24.12D14φ: C4×D7/C14C22 ⊆ Aut C23224C2^3:2(C4xD7)448,490
C233(C4×D7) = C24.24D14φ: C4×D7/C14C22 ⊆ Aut C23112C2^3:3(C4xD7)448,939
C234(C4×D7) = C2×Dic74D4φ: C4×D7/Dic7C2 ⊆ Aut C23224C2^3:4(C4xD7)448,938
C235(C4×D7) = C2×C4×C7⋊D4φ: C4×D7/C28C2 ⊆ Aut C23224C2^3:5(C4xD7)448,1241
C236(C4×D7) = C2×D7×C22⋊C4φ: C4×D7/D14C2 ⊆ Aut C23112C2^3:6(C4xD7)448,937

Non-split extensions G=N.Q with N=C23 and Q=C4×D7
extensionφ:Q→Aut NdρLabelID
C23.1(C4×D7) = C7⋊C2≀C4φ: C4×D7/D7C4 ⊆ Aut C23568+C2^3.1(C4xD7)448,28
C23.2(C4×D7) = (C2×C28).D4φ: C4×D7/D7C4 ⊆ Aut C231128-C2^3.2(C4xD7)448,29
C23.3(C4×D7) = C23.3D28φ: C4×D7/D7C4 ⊆ Aut C23568+C2^3.3(C4xD7)448,32
C23.4(C4×D7) = C23.4D28φ: C4×D7/D7C4 ⊆ Aut C231128-C2^3.4(C4xD7)448,33
C23.5(C4×D7) = C23⋊C45D7φ: C4×D7/D7C4 ⊆ Aut C231128-C2^3.5(C4xD7)448,274
C23.6(C4×D7) = D7×C4.D4φ: C4×D7/D7C4 ⊆ Aut C23568+C2^3.6(C4xD7)448,278
C23.7(C4×D7) = M4(2).19D14φ: C4×D7/D7C4 ⊆ Aut C231128-C2^3.7(C4xD7)448,279
C23.8(C4×D7) = C24.D14φ: C4×D7/C14C22 ⊆ Aut C23112C2^3.8(C4xD7)448,83
C23.9(C4×D7) = (C2×C56)⋊C4φ: C4×D7/C14C22 ⊆ Aut C231124C2^3.9(C4xD7)448,113
C23.10(C4×D7) = M4(2)⋊4Dic7φ: C4×D7/C14C22 ⊆ Aut C231124C2^3.10(C4xD7)448,116
C23.11(C4×D7) = C56⋊C4⋊C2φ: C4×D7/C14C22 ⊆ Aut C23224C2^3.11(C4xD7)448,254
C23.12(C4×D7) = D14⋊C8⋊C2φ: C4×D7/C14C22 ⊆ Aut C23224C2^3.12(C4xD7)448,261
C23.13(C4×D7) = D142M4(2)φ: C4×D7/C14C22 ⊆ Aut C23224C2^3.13(C4xD7)448,262
C23.14(C4×D7) = Dic7⋊M4(2)φ: C4×D7/C14C22 ⊆ Aut C23224C2^3.14(C4xD7)448,263
C23.15(C4×D7) = C24.3D14φ: C4×D7/C14C22 ⊆ Aut C23224C2^3.15(C4xD7)448,478
C23.16(C4×D7) = C24.4D14φ: C4×D7/C14C22 ⊆ Aut C23224C2^3.16(C4xD7)448,479
C23.17(C4×D7) = C2×C23.1D14φ: C4×D7/C14C22 ⊆ Aut C23112C2^3.17(C4xD7)448,488
C23.18(C4×D7) = C24.13D14φ: C4×D7/C14C22 ⊆ Aut C23224C2^3.18(C4xD7)448,491
C23.19(C4×D7) = C56⋊D4φ: C4×D7/C14C22 ⊆ Aut C23224C2^3.19(C4xD7)448,661
C23.20(C4×D7) = C5618D4φ: C4×D7/C14C22 ⊆ Aut C23224C2^3.20(C4xD7)448,662
C23.21(C4×D7) = M4(2).31D14φ: C4×D7/C14C22 ⊆ Aut C231124C2^3.21(C4xD7)448,666
C23.22(C4×D7) = C28.70C24φ: C4×D7/C14C22 ⊆ Aut C231124C2^3.22(C4xD7)448,1198
C23.23(C4×D7) = C7⋊D4⋊C8φ: C4×D7/Dic7C2 ⊆ Aut C23224C2^3.23(C4xD7)448,259
C23.24(C4×D7) = C7⋊C826D4φ: C4×D7/Dic7C2 ⊆ Aut C23224C2^3.24(C4xD7)448,264
C23.25(C4×D7) = C24.46D14φ: C4×D7/Dic7C2 ⊆ Aut C23224C2^3.25(C4xD7)448,480
C23.26(C4×D7) = C23.45D28φ: C4×D7/Dic7C2 ⊆ Aut C23224C2^3.26(C4xD7)448,492
C23.27(C4×D7) = C28.439(C2×D4)φ: C4×D7/Dic7C2 ⊆ Aut C23224C2^3.27(C4xD7)448,653
C23.28(C4×D7) = C28.7C42φ: C4×D7/Dic7C2 ⊆ Aut C23224C2^3.28(C4xD7)448,656
C23.29(C4×D7) = (C2×D28).14C4φ: C4×D7/Dic7C2 ⊆ Aut C23224C2^3.29(C4xD7)448,663
C23.30(C4×D7) = C2×D28.C4φ: C4×D7/Dic7C2 ⊆ Aut C23224C2^3.30(C4xD7)448,1197
C23.31(C4×D7) = C28.12C42φ: C4×D7/C28C2 ⊆ Aut C23224C2^3.31(C4xD7)448,635
C23.32(C4×D7) = Dic7⋊C8⋊C2φ: C4×D7/C28C2 ⊆ Aut C23224C2^3.32(C4xD7)448,636
C23.33(C4×D7) = C8×C7⋊D4φ: C4×D7/C28C2 ⊆ Aut C23224C2^3.33(C4xD7)448,643
C23.34(C4×D7) = (C22×C8)⋊D7φ: C4×D7/C28C2 ⊆ Aut C23224C2^3.34(C4xD7)448,644
C23.35(C4×D7) = C5632D4φ: C4×D7/C28C2 ⊆ Aut C23224C2^3.35(C4xD7)448,645
C23.36(C4×D7) = C4×C23.D7φ: C4×D7/C28C2 ⊆ Aut C23224C2^3.36(C4xD7)448,743
C23.37(C4×D7) = C24.62D14φ: C4×D7/C28C2 ⊆ Aut C23224C2^3.37(C4xD7)448,744
C23.38(C4×D7) = C23.28D28φ: C4×D7/C28C2 ⊆ Aut C23224C2^3.38(C4xD7)448,747
C23.39(C4×D7) = C2×D28.2C4φ: C4×D7/C28C2 ⊆ Aut C23224C2^3.39(C4xD7)448,1191
C23.40(C4×D7) = (C22×D7)⋊C8φ: C4×D7/D14C2 ⊆ Aut C23112C2^3.40(C4xD7)448,25
C23.41(C4×D7) = (C2×Dic7)⋊C8φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.41(C4xD7)448,26
C23.42(C4×D7) = C24.2D14φ: C4×D7/D14C2 ⊆ Aut C23112C2^3.42(C4xD7)448,84
C23.43(C4×D7) = M4(2)⋊Dic7φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.43(C4xD7)448,111
C23.44(C4×D7) = Dic7.5M4(2)φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.44(C4xD7)448,252
C23.45(C4×D7) = Dic7.M4(2)φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.45(C4xD7)448,253
C23.46(C4×D7) = D7×C22⋊C8φ: C4×D7/D14C2 ⊆ Aut C23112C2^3.46(C4xD7)448,258
C23.47(C4×D7) = D14⋊M4(2)φ: C4×D7/D14C2 ⊆ Aut C23112C2^3.47(C4xD7)448,260
C23.48(C4×D7) = C22⋊C4×Dic7φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.48(C4xD7)448,475
C23.49(C4×D7) = C24.44D14φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.49(C4xD7)448,476
C23.50(C4×D7) = C23.42D28φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.50(C4xD7)448,477
C23.51(C4×D7) = C23.44D28φ: C4×D7/D14C2 ⊆ Aut C23112C2^3.51(C4xD7)448,489
C23.52(C4×D7) = M4(2)×Dic7φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.52(C4xD7)448,651
C23.53(C4×D7) = Dic74M4(2)φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.53(C4xD7)448,652
C23.54(C4×D7) = D146M4(2)φ: C4×D7/D14C2 ⊆ Aut C23112C2^3.54(C4xD7)448,660
C23.55(C4×D7) = C2×C28.46D4φ: C4×D7/D14C2 ⊆ Aut C23112C2^3.55(C4xD7)448,664
C23.56(C4×D7) = C2×C4.12D28φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.56(C4xD7)448,670
C23.57(C4×D7) = C2×C23.11D14φ: C4×D7/D14C2 ⊆ Aut C23224C2^3.57(C4xD7)448,933
C23.58(C4×D7) = C2×D7×M4(2)φ: C4×D7/D14C2 ⊆ Aut C23112C2^3.58(C4xD7)448,1196
C23.59(C4×D7) = (C2×C56)⋊5C4central extension (φ=1)448C2^3.59(C4xD7)448,107
C23.60(C4×D7) = C2×C8×Dic7central extension (φ=1)448C2^3.60(C4xD7)448,632
C23.61(C4×D7) = C2×Dic7⋊C8central extension (φ=1)448C2^3.61(C4xD7)448,633
C23.62(C4×D7) = C2×C56⋊C4central extension (φ=1)448C2^3.62(C4xD7)448,634
C23.63(C4×D7) = C2×D14⋊C8central extension (φ=1)224C2^3.63(C4xD7)448,642
C23.64(C4×D7) = C2×C14.C42central extension (φ=1)448C2^3.64(C4xD7)448,742
C23.65(C4×D7) = D7×C22×C8central extension (φ=1)224C2^3.65(C4xD7)448,1189
C23.66(C4×D7) = C22×C8⋊D7central extension (φ=1)224C2^3.66(C4xD7)448,1190
C23.67(C4×D7) = C22×C4×Dic7central extension (φ=1)448C2^3.67(C4xD7)448,1235
C23.68(C4×D7) = C22×Dic7⋊C4central extension (φ=1)448C2^3.68(C4xD7)448,1236
C23.69(C4×D7) = C22×D14⋊C4central extension (φ=1)224C2^3.69(C4xD7)448,1240

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