Extensions 1→N→G→Q→1 with N=Q8 and Q=C2×C3⋊S3

Direct product G=N×Q with N=Q8 and Q=C2×C3⋊S3
dρLabelID
C2×Q8×C3⋊S3144C2xQ8xC3:S3288,1010

Semidirect products G=N:Q with N=Q8 and Q=C2×C3⋊S3
extensionφ:Q→Out NdρLabelID
Q8⋊(C2×C3⋊S3) = C2×C6.6S4φ: C2×C3⋊S3/C6 → S3 ⊆ Out Q848Q8:(C2xC3:S3)288,911
Q8⋊2(C2×C3⋊S3) = SD16×C3⋊S3φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out Q872Q8:2(C2xC3:S3)288,770
Q8⋊3(C2×C3⋊S3) = C24⋊7D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out Q872Q8:3(C2xC3:S3)288,771
Q8⋊4(C2×C3⋊S3) = C2×C32⋊11SD16φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out Q8144Q8:4(C2xC3:S3)288,798
Q8⋊5(C2×C3⋊S3) = C62.73D4φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out Q872Q8:5(C2xC3:S3)288,806
Q8⋊6(C2×C3⋊S3) = C2×C12.26D6φ: trivial image144Q8:6(C2xC3:S3)288,1011
Q8⋊7(C2×C3⋊S3) = C4○D4×C3⋊S3φ: trivial image72Q8:7(C2xC3:S3)288,1013
Q8⋊8(C2×C3⋊S3) = C62.154C23φ: trivial image72Q8:8(C2xC3:S3)288,1014

Non-split extensions G=N.Q with N=Q8 and Q=C2×C3⋊S3
extensionφ:Q→Out NdρLabelID
Q8.1(C2×C3⋊S3) = C2×C6.5S4φ: C2×C3⋊S3/C6 → S3 ⊆ Out Q896Q8.1(C2xC3:S3)288,910
Q8.2(C2×C3⋊S3) = SL2(𝔽3).D6φ: C2×C3⋊S3/C6 → S3 ⊆ Out Q8484Q8.2(C2xC3:S3)288,912
Q8.3(C2×C3⋊S3) = C12.6S4φ: C2×C3⋊S3/C6 → S3 ⊆ Out Q8964-Q8.3(C2xC3:S3)288,913
Q8.4(C2×C3⋊S3) = C12.14S4φ: C2×C3⋊S3/C6 → S3 ⊆ Out Q8484Q8.4(C2xC3:S3)288,914
Q8.5(C2×C3⋊S3) = C12.7S4φ: C2×C3⋊S3/C6 → S3 ⊆ Out Q8484+Q8.5(C2xC3:S3)288,915
Q8.6(C2×C3⋊S3) = C24.32D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out Q8144Q8.6(C2xC3:S3)288,772
Q8.7(C2×C3⋊S3) = C24.40D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out Q8144Q8.7(C2xC3:S3)288,773
Q8.8(C2×C3⋊S3) = Q16×C3⋊S3φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out Q8144Q8.8(C2xC3:S3)288,774
Q8.9(C2×C3⋊S3) = C24.35D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out Q8144Q8.9(C2xC3:S3)288,775
Q8.10(C2×C3⋊S3) = C24.28D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out Q8144Q8.10(C2xC3:S3)288,776
Q8.11(C2×C3⋊S3) = C62.134D4φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out Q8144Q8.11(C2xC3:S3)288,799
Q8.12(C2×C3⋊S3) = C2×C32⋊7Q16φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out Q8288Q8.12(C2xC3:S3)288,800
Q8.13(C2×C3⋊S3) = C62.74D4φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out Q8144Q8.13(C2xC3:S3)288,807
Q8.14(C2×C3⋊S3) = C62.75D4φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out Q8144Q8.14(C2xC3:S3)288,808
Q8.15(C2×C3⋊S3) = C32⋊72- 1+4φ: trivial image144Q8.15(C2xC3:S3)288,1012
Q8.16(C2×C3⋊S3) = C32⋊92- 1+4φ: trivial image144Q8.16(C2xC3:S3)288,1015

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