# Extensions 1→N→G→Q→1 with N=C23 and Q=C22

Direct product G=N×Q with N=C23 and Q=C22
dρLabelID
C2532C2^532,51

Semidirect products G=N:Q with N=C23 and Q=C22
extensionφ:Q→Aut NdρLabelID
C231C22 = C22≀C2φ: C22/C1C22 ⊆ Aut C238C2^3:1C2^232,27
C232C22 = 2+ 1+4φ: C22/C1C22 ⊆ Aut C2384+C2^3:2C2^232,49
C233C22 = C22×D4φ: C22/C2C2 ⊆ Aut C2316C2^3:3C2^232,46

Non-split extensions G=N.Q with N=C23 and Q=C22
extensionφ:Q→Aut NdρLabelID
C23.1C22 = C23⋊C4φ: C22/C1C22 ⊆ Aut C2384+C2^3.1C2^232,6
C23.2C22 = C4⋊D4φ: C22/C1C22 ⊆ Aut C2316C2^3.2C2^232,28
C23.3C22 = C4.4D4φ: C22/C1C22 ⊆ Aut C2316C2^3.3C2^232,31
C23.4C22 = C422C2φ: C22/C1C22 ⊆ Aut C2316C2^3.4C2^232,33
C23.5C22 = C41D4φ: C22/C1C22 ⊆ Aut C2316C2^3.5C2^232,34
C23.6C22 = C2×C22⋊C4φ: C22/C2C2 ⊆ Aut C2316C2^3.6C2^232,22
C23.7C22 = C42⋊C2φ: C22/C2C2 ⊆ Aut C2316C2^3.7C2^232,24
C23.8C22 = C4×D4φ: C22/C2C2 ⊆ Aut C2316C2^3.8C2^232,25
C23.9C22 = C22⋊Q8φ: C22/C2C2 ⊆ Aut C2316C2^3.9C2^232,29
C23.10C22 = C22.D4φ: C22/C2C2 ⊆ Aut C2316C2^3.10C2^232,30
C23.11C22 = C2×C4○D4φ: C22/C2C2 ⊆ Aut C2316C2^3.11C2^232,48
C23.12C22 = C2.C42central extension (φ=1)32C2^3.12C2^232,2
C23.13C22 = C2×C4⋊C4central extension (φ=1)32C2^3.13C2^232,23
C23.14C22 = C22×Q8central extension (φ=1)32C2^3.14C2^232,47

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