# Extensions 1→N→G→Q→1 with N=C23 and Q=C2×Dic7

Direct product G=N×Q with N=C23 and Q=C2×Dic7
dρLabelID
C24×Dic7448C2^4xDic7448,1383

Semidirect products G=N:Q with N=C23 and Q=C2×Dic7
extensionφ:Q→Aut NdρLabelID
C231(C2×Dic7) = C2×C23⋊Dic7φ: C2×Dic7/C14C4 ⊆ Aut C23112C2^3:1(C2xDic7)448,753
C232(C2×Dic7) = C24.18D14φ: C2×Dic7/C14C22 ⊆ Aut C23224C2^3:2(C2xDic7)448,754
C233(C2×Dic7) = C24.38D14φ: C2×Dic7/C14C22 ⊆ Aut C23112C2^3:3(C2xDic7)448,1251
C234(C2×Dic7) = C2×D4×Dic7φ: C2×Dic7/Dic7C2 ⊆ Aut C23224C2^3:4(C2xDic7)448,1248
C235(C2×Dic7) = C22×C23.D7φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3:5(C2xDic7)448,1292

Non-split extensions G=N.Q with N=C23 and Q=C2×Dic7
extensionφ:Q→Aut NdρLabelID
C23.1(C2×Dic7) = C24⋊Dic7φ: C2×Dic7/C14C4 ⊆ Aut C23564C2^3.1(C2xDic7)448,93
C23.2(C2×Dic7) = (C22×C28)⋊C4φ: C2×Dic7/C14C4 ⊆ Aut C231124C2^3.2(C2xDic7)448,96
C23.3(C2×Dic7) = (D4×C14).16C4φ: C2×Dic7/C14C4 ⊆ Aut C231124C2^3.3(C2xDic7)448,771
C23.4(C2×Dic7) = (D4×C14)⋊10C4φ: C2×Dic7/C14C4 ⊆ Aut C231124C2^3.4(C2xDic7)448,774
C23.5(C2×Dic7) = C24.2D14φ: C2×Dic7/C14C22 ⊆ Aut C23112C2^3.5(C2xDic7)448,84
C23.6(C2×Dic7) = (C2×C28).Q8φ: C2×Dic7/C14C22 ⊆ Aut C231124C2^3.6(C2xDic7)448,90
C23.7(C2×Dic7) = C24.8D14φ: C2×Dic7/C14C22 ⊆ Aut C23224C2^3.7(C2xDic7)448,485
C23.8(C2×Dic7) = C42.187D14φ: C2×Dic7/C14C22 ⊆ Aut C23224C2^3.8(C2xDic7)448,534
C23.9(C2×Dic7) = C283M4(2)φ: C2×Dic7/C14C22 ⊆ Aut C23224C2^3.9(C2xDic7)448,546
C23.10(C2×Dic7) = C24.19D14φ: C2×Dic7/C14C22 ⊆ Aut C23224C2^3.10(C2xDic7)448,755
C23.11(C2×Dic7) = C28.76C24φ: C2×Dic7/C14C22 ⊆ Aut C231124C2^3.11(C2xDic7)448,1272
C23.12(C2×Dic7) = C22⋊C4×Dic7φ: C2×Dic7/Dic7C2 ⊆ Aut C23224C2^3.12(C2xDic7)448,475
C23.13(C2×Dic7) = C24.47D14φ: C2×Dic7/Dic7C2 ⊆ Aut C23224C2^3.13(C2xDic7)448,484
C23.14(C2×Dic7) = C28.5C42φ: C2×Dic7/Dic7C2 ⊆ Aut C23224C2^3.14(C2xDic7)448,531
C23.15(C2×Dic7) = C42.43D14φ: C2×Dic7/Dic7C2 ⊆ Aut C23224C2^3.15(C2xDic7)448,533
C23.16(C2×Dic7) = D4×C7⋊C8φ: C2×Dic7/Dic7C2 ⊆ Aut C23224C2^3.16(C2xDic7)448,544
C23.17(C2×Dic7) = C42.47D14φ: C2×Dic7/Dic7C2 ⊆ Aut C23224C2^3.17(C2xDic7)448,545
C23.18(C2×Dic7) = (D4×C14).11C4φ: C2×Dic7/Dic7C2 ⊆ Aut C23224C2^3.18(C2xDic7)448,768
C23.19(C2×Dic7) = C2×Q8.Dic7φ: C2×Dic7/Dic7C2 ⊆ Aut C23224C2^3.19(C2xDic7)448,1271
C23.20(C2×Dic7) = C24.Dic7φ: C2×Dic7/C2×C14C2 ⊆ Aut C23112C2^3.20(C2xDic7)448,82
C23.21(C2×Dic7) = C24.D14φ: C2×Dic7/C2×C14C2 ⊆ Aut C23112C2^3.21(C2xDic7)448,83
C23.22(C2×Dic7) = (C2×C28)⋊C8φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.22(C2xDic7)448,85
C23.23(C2×Dic7) = C28.(C4⋊C4)φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.23(C2xDic7)448,87
C23.24(C2×Dic7) = C4×C4.Dic7φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.24(C2xDic7)448,456
C23.25(C2×Dic7) = C287M4(2)φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.25(C2xDic7)448,458
C23.26(C2×Dic7) = C42.6Dic7φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.26(C2xDic7)448,459
C23.27(C2×Dic7) = C42.7Dic7φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.27(C2xDic7)448,460
C23.28(C2×Dic7) = C24.4Dic7φ: C2×Dic7/C2×C14C2 ⊆ Aut C23112C2^3.28(C2xDic7)448,741
C23.29(C2×Dic7) = C4×C23.D7φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.29(C2xDic7)448,743
C23.30(C2×Dic7) = C24.63D14φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.30(C2xDic7)448,745
C23.31(C2×Dic7) = C23.27D28φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.31(C2xDic7)448,746
C23.32(C2×Dic7) = C2×C28.D4φ: C2×Dic7/C2×C14C2 ⊆ Aut C23112C2^3.32(C2xDic7)448,750
C23.33(C2×Dic7) = C2×C28.10D4φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.33(C2xDic7)448,760
C23.34(C2×Dic7) = C25.D7φ: C2×Dic7/C2×C14C2 ⊆ Aut C23112C2^3.34(C2xDic7)448,781
C23.35(C2×Dic7) = C22×C4.Dic7φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.35(C2xDic7)448,1234
C23.36(C2×Dic7) = C2×C23.21D14φ: C2×Dic7/C2×C14C2 ⊆ Aut C23224C2^3.36(C2xDic7)448,1239
C23.37(C2×Dic7) = (C2×C28)⋊3C8central extension (φ=1)448C2^3.37(C2xDic7)448,81
C23.38(C2×Dic7) = C2×C4×C7⋊C8central extension (φ=1)448C2^3.38(C2xDic7)448,454
C23.39(C2×Dic7) = C2×C42.D7central extension (φ=1)448C2^3.39(C2xDic7)448,455
C23.40(C2×Dic7) = C2×C28⋊C8central extension (φ=1)448C2^3.40(C2xDic7)448,457
C23.41(C2×Dic7) = C2×C28.55D4central extension (φ=1)224C2^3.41(C2xDic7)448,740
C23.42(C2×Dic7) = C2×C14.C42central extension (φ=1)448C2^3.42(C2xDic7)448,742
C23.43(C2×Dic7) = C23×C7⋊C8central extension (φ=1)448C2^3.43(C2xDic7)448,1233
C23.44(C2×Dic7) = C22×C4×Dic7central extension (φ=1)448C2^3.44(C2xDic7)448,1235
C23.45(C2×Dic7) = C22×C4⋊Dic7central extension (φ=1)448C2^3.45(C2xDic7)448,1238

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