# Extensions 1→N→G→Q→1 with N=C9○He3 and Q=C6

Direct product G=N×Q with N=C9○He3 and Q=C6
dρLabelID
C6×C9○He3162C6xC9oHe3486,253

Semidirect products G=N:Q with N=C9○He3 and Q=C6
extensionφ:Q→Out NdρLabelID
C9○He31C6 = 3- 1+4⋊C2φ: C6/C1C6 ⊆ Out C9○He32718+C9oHe3:1C6486,238
C9○He32C6 = C3≀S33C3φ: C6/C1C6 ⊆ Out C9○He3273C9oHe3:2C6486,125
C9○He33C6 = C3≀C3.C6φ: C6/C1C6 ⊆ Out C9○He3279C9oHe3:3C6486,132
C9○He34C6 = 3- 1+42C2φ: C6/C1C6 ⊆ Out C9○He3279C9oHe3:4C6486,239
C9○He35C6 = C2×C9.He3φ: C6/C2C3 ⊆ Out C9○He3543C9oHe3:5C6486,214
C9○He36C6 = C2×C9.2He3φ: C6/C2C3 ⊆ Out C9○He3549C9oHe3:6C6486,219
C9○He37C6 = C2×3- 1+4φ: C6/C2C3 ⊆ Out C9○He3549C9oHe3:7C6486,255
C9○He38C6 = C3×He3.4S3φ: C6/C3C2 ⊆ Out C9○He3546C9oHe3:8C6486,234
C9○He39C6 = C3×He3.4C6φ: C6/C3C2 ⊆ Out C9○He381C9oHe3:9C6486,235

Non-split extensions G=N.Q with N=C9○He3 and Q=C6
extensionφ:Q→Out NdρLabelID
C9○He3.1C6 = He3.C18φ: C6/C1C6 ⊆ Out C9○He3813C9oHe3.1C6486,26
C9○He3.2C6 = He3.2C18φ: C6/C1C6 ⊆ Out C9○He3813C9oHe3.2C6486,28
C9○He3.3C6 = C2×C9.5He3φ: C6/C2C3 ⊆ Out C9○He31623C9oHe3.3C6486,79
C9○He3.4C6 = C2×C9.6He3φ: C6/C2C3 ⊆ Out C9○He31623C9oHe3.4C6486,80
C9○He3.5C6 = He3.5C18φ: C6/C3C2 ⊆ Out C9○He3813C9oHe3.5C6486,164
C9○He3.6C6 = C2×C27○He3φ: trivial image1623C9oHe3.6C6486,209

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