Extensions 1→N→G→Q→1 with N=He3 and Q=C6

Direct product G=NxQ with N=He3 and Q=C6
dρLabelID
C6xHe354C6xHe3162,48

Semidirect products G=N:Q with N=He3 and Q=C6
extensionφ:Q→Out NdρLabelID
He3:C6 = C3wrS3φ: C6/C1C6 ⊆ Out He393He3:C6162,10
He3:2C6 = C2xC3wrC3φ: C6/C2C3 ⊆ Out He3183He3:2C6162,28
He3:3C6 = C2xHe3:C3φ: C6/C2C3 ⊆ Out He3543He3:3C6162,30
He3:4C6 = C3xC32:C6φ: C6/C3C2 ⊆ Out He3186He3:4C6162,34
He3:5C6 = C3xHe3:C2φ: C6/C3C2 ⊆ Out He327He3:5C6162,41

Non-split extensions G=N.Q with N=He3 and Q=C6
extensionφ:Q→Out NdρLabelID
He3.1C6 = He3.C6φ: C6/C1C6 ⊆ Out He3273He3.1C6162,12
He3.2C6 = He3.2C6φ: C6/C1C6 ⊆ Out He3273He3.2C6162,14
He3.3C6 = C2xHe3.C3φ: C6/C2C3 ⊆ Out He3543He3.3C6162,29
He3.4C6 = He3.4C6φ: C6/C3C2 ⊆ Out He3273He3.4C6162,44
He3.5C6 = C2xC9oHe3φ: trivial image543He3.5C6162,50

׿
x
:
Z
F
o
wr
Q
<