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Extensions 1→N→G→Q→1 with N=C6 and Q=Q8⋊2S3

Direct product G=N×Q with N=C6 and Q=Q8⋊2S3
dρLabelID
C6×Q8⋊2S396C6xQ8:2S3288,712

Semidirect products G=N:Q with N=C6 and Q=Q8⋊2S3
extensionφ:Q→Aut NdρLabelID
C6⋊1(Q8⋊2S3) = C2×C32⋊5SD16φ: Q8⋊2S3/C3⋊C8 → C2 ⊆ Aut C648C6:1(Q8:2S3)288,480
C6⋊2(Q8⋊2S3) = C2×Dic6⋊S3φ: Q8⋊2S3/D12 → C2 ⊆ Aut C696C6:2(Q8:2S3)288,474
C6⋊3(Q8⋊2S3) = C2×C32⋊11SD16φ: Q8⋊2S3/C3×Q8 → C2 ⊆ Aut C6144C6:3(Q8:2S3)288,798

Non-split extensions G=N.Q with N=C6 and Q=Q8⋊2S3
extensionφ:Q→Aut NdρLabelID
C6.1(Q8⋊2S3) = C6.17D24φ: Q8⋊2S3/C3⋊C8 → C2 ⊆ Aut C648C6.1(Q8:2S3)288,212
C6.2(Q8⋊2S3) = C6.Dic12φ: Q8⋊2S3/C3⋊C8 → C2 ⊆ Aut C696C6.2(Q8:2S3)288,214
C6.3(Q8⋊2S3) = C12.Dic6φ: Q8⋊2S3/C3⋊C8 → C2 ⊆ Aut C696C6.3(Q8:2S3)288,221
C6.4(Q8⋊2S3) = D12⋊3Dic3φ: Q8⋊2S3/D12 → C2 ⊆ Aut C696C6.4(Q8:2S3)288,210
C6.5(Q8⋊2S3) = Dic6⋊Dic3φ: Q8⋊2S3/D12 → C2 ⊆ Aut C696C6.5(Q8:2S3)288,213
C6.6(Q8⋊2S3) = C12.6Dic6φ: Q8⋊2S3/D12 → C2 ⊆ Aut C696C6.6(Q8:2S3)288,222
C6.7(Q8⋊2S3) = C4.Dic18φ: Q8⋊2S3/C3×Q8 → C2 ⊆ Aut C6288C6.7(Q8:2S3)288,15
C6.8(Q8⋊2S3) = C18.D8φ: Q8⋊2S3/C3×Q8 → C2 ⊆ Aut C6144C6.8(Q8:2S3)288,17
C6.9(Q8⋊2S3) = Q8⋊2Dic9φ: Q8⋊2S3/C3×Q8 → C2 ⊆ Aut C6288C6.9(Q8:2S3)288,43
C6.10(Q8⋊2S3) = C2×Q8⋊2D9φ: Q8⋊2S3/C3×Q8 → C2 ⊆ Aut C6144C6.10(Q8:2S3)288,152
C6.11(Q8⋊2S3) = C12.10Dic6φ: Q8⋊2S3/C3×Q8 → C2 ⊆ Aut C6288C6.11(Q8:2S3)288,283
C6.12(Q8⋊2S3) = C62.113D4φ: Q8⋊2S3/C3×Q8 → C2 ⊆ Aut C6144C6.12(Q8:2S3)288,284
C6.13(Q8⋊2S3) = C62.117D4φ: Q8⋊2S3/C3×Q8 → C2 ⊆ Aut C6288C6.13(Q8:2S3)288,310
C6.14(Q8⋊2S3) = C3×C12.Q8central extension (φ=1)96C6.14(Q8:2S3)288,242
C6.15(Q8⋊2S3) = C3×C6.D8central extension (φ=1)96C6.15(Q8:2S3)288,243
C6.16(Q8⋊2S3) = C3×Q8⋊2Dic3central extension (φ=1)96C6.16(Q8:2S3)288,269

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