# Extensions 1→N→G→Q→1 with N=C32 and Q=He3

Direct product G=N×Q with N=C32 and Q=He3
dρLabelID
C32×He381C3^2xHe3243,62

Semidirect products G=N:Q with N=C32 and Q=He3
extensionφ:Q→Aut NdρLabelID
C32⋊He3 = C32⋊He3φ: He3/C32C3 ⊆ Aut C3227C3^2:He3243,37

Non-split extensions G=N.Q with N=C32 and Q=He3
extensionφ:Q→Aut NdρLabelID
C32.1He3 = C92⋊C3φ: He3/C32C3 ⊆ Aut C32273C3^2.1He3243,25
C32.2He3 = C922C3φ: He3/C32C3 ⊆ Aut C32273C3^2.2He3243,26
C32.3He3 = C92.C3φ: He3/C32C3 ⊆ Aut C32273C3^2.3He3243,27
C32.4He3 = C32.He3φ: He3/C32C3 ⊆ Aut C32279C3^2.4He3243,28
C32.5He3 = C32.5He3φ: He3/C32C3 ⊆ Aut C32279C3^2.5He3243,29
C32.6He3 = C32.6He3φ: He3/C32C3 ⊆ Aut C32279C3^2.6He3243,30
C32.7He3 = C34.C3φ: He3/C32C3 ⊆ Aut C3227C3^2.7He3243,38
C32.8He3 = C32.23C33φ: He3/C32C3 ⊆ Aut C3281C3^2.8He3243,40
C32.9He3 = C3×C3≀C3φ: He3/C32C3 ⊆ Aut C3227C3^2.9He3243,51
C32.10He3 = C3×He3.C3φ: He3/C32C3 ⊆ Aut C3281C3^2.10He3243,52
C32.11He3 = C3×He3⋊C3φ: He3/C32C3 ⊆ Aut C3281C3^2.11He3243,53
C32.12He3 = C3×C3.He3φ: He3/C32C3 ⊆ Aut C3281C3^2.12He3243,54
C32.13He3 = C33⋊C32φ: He3/C32C3 ⊆ Aut C32279C3^2.13He3243,56
C32.14He3 = He3.C32φ: He3/C32C3 ⊆ Aut C32279C3^2.14He3243,57
C32.15He3 = He3⋊C32φ: He3/C32C3 ⊆ Aut C32279C3^2.15He3243,58
C32.16He3 = C32.C33φ: He3/C32C3 ⊆ Aut C32279C3^2.16He3243,59
C32.17He3 = C3.C92central extension (φ=1)243C3^2.17He3243,2
C32.18He3 = C33⋊C9central extension (φ=1)27C3^2.18He3243,13
C32.19He3 = C32.19He3central extension (φ=1)81C3^2.19He3243,14
C32.20He3 = C32.20He3central extension (φ=1)81C3^2.20He3243,15
C32.21He3 = He3⋊C9central extension (φ=1)81C3^2.21He3243,17
C32.22He3 = 3- 1+2⋊C9central extension (φ=1)81C3^2.22He3243,18
C32.23He3 = C3×C32⋊C9central extension (φ=1)81C3^2.23He3243,32
C32.24He3 = C32.24He3central stem extension (φ=1)81C3^2.24He3243,3
C32.25He3 = C33.C32central stem extension (φ=1)81C3^2.25He3243,4
C32.26He3 = C33.3C32central stem extension (φ=1)81C3^2.26He3243,5
C32.27He3 = C32.27He3central stem extension (φ=1)81C3^2.27He3243,6
C32.28He3 = C32.28He3central stem extension (φ=1)81C3^2.28He3243,7
C32.29He3 = C32.29He3central stem extension (φ=1)81C3^2.29He3243,8
C32.30He3 = C33.7C32central stem extension (φ=1)81C3^2.30He3243,9

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