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Extensions 1→N→G→Q→1 with N=Q8 and Q=C3⋊D4

Direct product G=N×Q with N=Q8 and Q=C3⋊D4
dρLabelID
Q8×C3⋊D496Q8xC3:D4192,1374

Semidirect products G=N:Q with N=Q8 and Q=C3⋊D4
extensionφ:Q→Out NdρLabelID
Q8⋊(C3⋊D4) = C23.16S4φ: C3⋊D4/C22 → S3 ⊆ Out Q832Q8:(C3:D4)192,980
Q8⋊2(C3⋊D4) = Dic3⋊5SD16φ: C3⋊D4/Dic3 → C2 ⊆ Out Q896Q8:2(C3:D4)192,722
Q8⋊3(C3⋊D4) = D6⋊8SD16φ: C3⋊D4/D6 → C2 ⊆ Out Q896Q8:3(C3:D4)192,729
Q8⋊4(C3⋊D4) = D12⋊7D4φ: C3⋊D4/D6 → C2 ⊆ Out Q896Q8:4(C3:D4)192,731
Q8⋊5(C3⋊D4) = D12⋊18D4φ: C3⋊D4/D6 → C2 ⊆ Out Q8248+Q8:5(C3:D4)192,757
Q8⋊6(C3⋊D4) = (C3×Q8)⋊13D4φ: C3⋊D4/C2×C6 → C2 ⊆ Out Q896Q8:6(C3:D4)192,786
Q8⋊7(C3⋊D4) = (C3×D4)⋊14D4φ: C3⋊D4/C2×C6 → C2 ⊆ Out Q896Q8:7(C3:D4)192,797
Q8⋊8(C3⋊D4) = 2+ 1+4⋊6S3φ: C3⋊D4/C2×C6 → C2 ⊆ Out Q8248+Q8:8(C3:D4)192,800
Q8⋊9(C3⋊D4) = C6.452- 1+4φ: trivial image96Q8:9(C3:D4)192,1376
Q8⋊10(C3⋊D4) = C6.1072- 1+4φ: trivial image96Q8:10(C3:D4)192,1390
Q8⋊11(C3⋊D4) = C6.1482+ 1+4φ: trivial image96Q8:11(C3:D4)192,1393

Non-split extensions G=N.Q with N=Q8 and Q=C3⋊D4
extensionφ:Q→Out NdρLabelID
Q8.1(C3⋊D4) = C23.14S4φ: C3⋊D4/C22 → S3 ⊆ Out Q832Q8.1(C3:D4)192,978
Q8.2(C3⋊D4) = SL2(𝔽3).D4φ: C3⋊D4/C22 → S3 ⊆ Out Q864Q8.2(C3:D4)192,984
Q8.3(C3⋊D4) = SL2(𝔽3)⋊D4φ: C3⋊D4/C22 → S3 ⊆ Out Q832Q8.3(C3:D4)192,986
Q8.4(C3⋊D4) = Q8.4S4φ: C3⋊D4/C22 → S3 ⊆ Out Q8484Q8.4(C3:D4)192,987
Q8.5(C3⋊D4) = Q8.5S4φ: C3⋊D4/C22 → S3 ⊆ Out Q8244+Q8.5(C3:D4)192,988
Q8.6(C3⋊D4) = D4.S4φ: C3⋊D4/C22 → S3 ⊆ Out Q8324-Q8.6(C3:D4)192,989
Q8.7(C3⋊D4) = D4.3S4φ: C3⋊D4/C22 → S3 ⊆ Out Q8324Q8.7(C3:D4)192,990
Q8.8(C3⋊D4) = (C3×Q8).D4φ: C3⋊D4/Dic3 → C2 ⊆ Out Q896Q8.8(C3:D4)192,725
Q8.9(C3⋊D4) = Dic3⋊3Q16φ: C3⋊D4/Dic3 → C2 ⊆ Out Q8192Q8.9(C3:D4)192,741
Q8.10(C3⋊D4) = (C2×Q16)⋊S3φ: C3⋊D4/Dic3 → C2 ⊆ Out Q896Q8.10(C3:D4)192,744
Q8.11(C3⋊D4) = M4(2).D6φ: C3⋊D4/Dic3 → C2 ⊆ Out Q8488+Q8.11(C3:D4)192,758
Q8.12(C3⋊D4) = M4(2).13D6φ: C3⋊D4/Dic3 → C2 ⊆ Out Q8488-Q8.12(C3:D4)192,759
Q8.13(C3⋊D4) = M4(2).15D6φ: C3⋊D4/Dic3 → C2 ⊆ Out Q8488+Q8.13(C3:D4)192,762
Q8.14(C3⋊D4) = M4(2).16D6φ: C3⋊D4/Dic3 → C2 ⊆ Out Q8968-Q8.14(C3:D4)192,763
Q8.15(C3⋊D4) = D6⋊5Q16φ: C3⋊D4/D6 → C2 ⊆ Out Q896Q8.15(C3:D4)192,745
Q8.16(C3⋊D4) = D12.17D4φ: C3⋊D4/D6 → C2 ⊆ Out Q896Q8.16(C3:D4)192,746
Q8.17(C3⋊D4) = D12.38D4φ: C3⋊D4/D6 → C2 ⊆ Out Q8488-Q8.17(C3:D4)192,760
Q8.18(C3⋊D4) = D12.39D4φ: C3⋊D4/D6 → C2 ⊆ Out Q8488+Q8.18(C3:D4)192,761
Q8.19(C3⋊D4) = D12.40D4φ: C3⋊D4/D6 → C2 ⊆ Out Q8488-Q8.19(C3:D4)192,764
Q8.20(C3⋊D4) = (C2×C6)⋊8Q16φ: C3⋊D4/C2×C6 → C2 ⊆ Out Q896Q8.20(C3:D4)192,787
Q8.21(C3⋊D4) = (C3×D4).32D4φ: C3⋊D4/C2×C6 → C2 ⊆ Out Q896Q8.21(C3:D4)192,798
Q8.22(C3⋊D4) = 2+ 1+4.4S3φ: C3⋊D4/C2×C6 → C2 ⊆ Out Q8488-Q8.22(C3:D4)192,801
Q8.23(C3⋊D4) = 2- 1+4⋊4S3φ: C3⋊D4/C2×C6 → C2 ⊆ Out Q8488+Q8.23(C3:D4)192,804
Q8.24(C3⋊D4) = 2- 1+4.2S3φ: C3⋊D4/C2×C6 → C2 ⊆ Out Q8488-Q8.24(C3:D4)192,805
Q8.25(C3⋊D4) = D12.32C23φ: trivial image488+Q8.25(C3:D4)192,1394
Q8.26(C3⋊D4) = D12.33C23φ: trivial image488-Q8.26(C3:D4)192,1395
Q8.27(C3⋊D4) = D12.34C23φ: trivial image488+Q8.27(C3:D4)192,1396
Q8.28(C3⋊D4) = D12.35C23φ: trivial image968-Q8.28(C3:D4)192,1397

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