Extensions 1→N→G→Q→1 with N=Q8 and Q=He3⋊C2

Direct product G=N×Q with N=Q8 and Q=He3⋊C2
dρLabelID
Q8×He3⋊C2726Q8xHe3:C2432,394

Semidirect products G=N:Q with N=Q8 and Q=He3⋊C2
extensionφ:Q→Out NdρLabelID
Q8⋊(He3⋊C2) = C323GL2(𝔽3)φ: He3⋊C2/C32S3 ⊆ Out Q8726Q8:(He3:C2)432,258
Q82(He3⋊C2) = He311SD16φ: He3⋊C2/He3C2 ⊆ Out Q8726Q8:2(He3:C2)432,196
Q83(He3⋊C2) = He35D4⋊C2φ: trivial image726Q8:3(He3:C2)432,395

Non-split extensions G=N.Q with N=Q8 and Q=He3⋊C2
extensionφ:Q→Out NdρLabelID
Q8.(He3⋊C2) = C322CSU2(𝔽3)φ: He3⋊C2/C32S3 ⊆ Out Q81446Q8.(He3:C2)432,257
Q8.2(He3⋊C2) = He37Q16φ: He3⋊C2/He3C2 ⊆ Out Q81446Q8.2(He3:C2)432,197

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