# Extensions 1→N→G→Q→1 with N=C24 and Q=C2×C6

Direct product G=N×Q with N=C24 and Q=C2×C6
dρLabelID
C25×C6192C2^5xC6192,1543

Semidirect products G=N:Q with N=C24 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C24⋊(C2×C6) = C24⋊A4φ: C2×C6/C1C2×C6 ⊆ Aut C241612+C2^4:(C2xC6)192,1009
C242(C2×C6) = C2×C24⋊C6φ: C2×C6/C2C6 ⊆ Aut C24126+C2^4:2(C2xC6)192,1000
C243(C2×C6) = C2×D4×A4φ: C2×C6/C2C6 ⊆ Aut C2424C2^4:3(C2xC6)192,1497
C244(C2×C6) = C3×C2≀C22φ: C2×C6/C3C22 ⊆ Aut C24244C2^4:4(C2xC6)192,890
C245(C2×C6) = C3×C233D4φ: C2×C6/C3C22 ⊆ Aut C2448C2^4:5(C2xC6)192,1423
C246(C2×C6) = C3×D42φ: C2×C6/C3C22 ⊆ Aut C2448C2^4:6(C2xC6)192,1434
C247(C2×C6) = C3×C24⋊C22φ: C2×C6/C3C22 ⊆ Aut C2448C2^4:7(C2xC6)192,1450
C248(C2×C6) = C6×2+ 1+4φ: C2×C6/C3C22 ⊆ Aut C2448C2^4:8(C2xC6)192,1534
C249(C2×C6) = A4×C24φ: C2×C6/C22C3 ⊆ Aut C2448C2^4:9(C2xC6)192,1539
C2410(C2×C6) = C22×C22⋊A4φ: C2×C6/C22C3 ⊆ Aut C2412C2^4:10(C2xC6)192,1540
C2411(C2×C6) = C6×C22≀C2φ: C2×C6/C6C2 ⊆ Aut C2448C2^4:11(C2xC6)192,1410
C2412(C2×C6) = D4×C22×C6φ: C2×C6/C6C2 ⊆ Aut C2496C2^4:12(C2xC6)192,1531

Non-split extensions G=N.Q with N=C24 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C24.(C2×C6) = A4×C4○D4φ: C2×C6/C2C6 ⊆ Aut C24246C2^4.(C2xC6)192,1501
C24.2(C2×C6) = C3×C23.9D4φ: C2×C6/C3C22 ⊆ Aut C2448C2^4.2(C2xC6)192,148
C24.3(C2×C6) = C3×C24.C22φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.3(C2xC6)192,821
C24.4(C2×C6) = C3×C24.3C22φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.4(C2xC6)192,823
C24.5(C2×C6) = C3×C232D4φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.5(C2xC6)192,825
C24.6(C2×C6) = C3×C23⋊Q8φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.6(C2xC6)192,826
C24.7(C2×C6) = C3×C23.10D4φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.7(C2xC6)192,827
C24.8(C2×C6) = C3×C23.Q8φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.8(C2xC6)192,829
C24.9(C2×C6) = C3×C23.11D4φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.9(C2xC6)192,830
C24.10(C2×C6) = C3×C23.4Q8φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.10(C2xC6)192,832
C24.11(C2×C6) = C6×C23⋊C4φ: C2×C6/C3C22 ⊆ Aut C2448C2^4.11(C2xC6)192,842
C24.12(C2×C6) = C3×C22.11C24φ: C2×C6/C3C22 ⊆ Aut C2448C2^4.12(C2xC6)192,1407
C24.13(C2×C6) = C6×C4⋊D4φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.13(C2xC6)192,1411
C24.14(C2×C6) = C6×C4.4D4φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.14(C2xC6)192,1415
C24.15(C2×C6) = C6×C422C2φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.15(C2xC6)192,1417
C24.16(C2×C6) = C6×C41D4φ: C2×C6/C3C22 ⊆ Aut C2496C2^4.16(C2xC6)192,1419
C24.17(C2×C6) = C3×C22.29C24φ: C2×C6/C3C22 ⊆ Aut C2448C2^4.17(C2xC6)192,1424
C24.18(C2×C6) = C3×C22.32C24φ: C2×C6/C3C22 ⊆ Aut C2448C2^4.18(C2xC6)192,1427
C24.19(C2×C6) = C3×C232Q8φ: C2×C6/C3C22 ⊆ Aut C2448C2^4.19(C2xC6)192,1432
C24.20(C2×C6) = C3×D45D4φ: C2×C6/C3C22 ⊆ Aut C2448C2^4.20(C2xC6)192,1435
C24.21(C2×C6) = C3×C22.45C24φ: C2×C6/C3C22 ⊆ Aut C2448C2^4.21(C2xC6)192,1440
C24.22(C2×C6) = C3×C22.54C24φ: C2×C6/C3C22 ⊆ Aut C2448C2^4.22(C2xC6)192,1449
C24.23(C2×C6) = A4×C42φ: C2×C6/C22C3 ⊆ Aut C2448C2^4.23(C2xC6)192,993
C24.24(C2×C6) = A4×C22⋊C4φ: C2×C6/C22C3 ⊆ Aut C2424C2^4.24(C2xC6)192,994
C24.25(C2×C6) = A4×C4⋊C4φ: C2×C6/C22C3 ⊆ Aut C2448C2^4.25(C2xC6)192,995
C24.26(C2×C6) = A4×C22×C4φ: C2×C6/C22C3 ⊆ Aut C2448C2^4.26(C2xC6)192,1496
C24.27(C2×C6) = C2×Q8×A4φ: C2×C6/C22C3 ⊆ Aut C2448C2^4.27(C2xC6)192,1499
C24.28(C2×C6) = C12×C22⋊C4φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.28(C2xC6)192,810
C24.29(C2×C6) = C3×C243C4φ: C2×C6/C6C2 ⊆ Aut C2448C2^4.29(C2xC6)192,812
C24.30(C2×C6) = C3×C23.7Q8φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.30(C2xC6)192,813
C24.31(C2×C6) = C3×C23.34D4φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.31(C2xC6)192,814
C24.32(C2×C6) = C3×C23.8Q8φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.32(C2xC6)192,818
C24.33(C2×C6) = C3×C23.23D4φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.33(C2xC6)192,819
C24.34(C2×C6) = C2×C6×C22⋊C4φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.34(C2xC6)192,1401
C24.35(C2×C6) = C6×C42⋊C2φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.35(C2xC6)192,1403
C24.36(C2×C6) = D4×C2×C12φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.36(C2xC6)192,1404
C24.37(C2×C6) = C6×C22⋊Q8φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.37(C2xC6)192,1412
C24.38(C2×C6) = C6×C22.D4φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.38(C2xC6)192,1413
C24.39(C2×C6) = C3×C22.19C24φ: C2×C6/C6C2 ⊆ Aut C2448C2^4.39(C2xC6)192,1414
C24.40(C2×C6) = C2×C6×C4○D4φ: C2×C6/C6C2 ⊆ Aut C2496C2^4.40(C2xC6)192,1533
C24.41(C2×C6) = C6×C2.C42central extension (φ=1)192C2^4.41(C2xC6)192,808
C24.42(C2×C6) = C2×C6×C4⋊C4central extension (φ=1)192C2^4.42(C2xC6)192,1402
C24.43(C2×C6) = Q8×C22×C6central extension (φ=1)192C2^4.43(C2xC6)192,1532

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