# Extensions 1→N→G→Q→1 with N=C24 and Q=C6

Direct product G=N×Q with N=C24 and Q=C6
dρLabelID
C6×C24144C6xC24144,104

Semidirect products G=N:Q with N=C24 and Q=C6
extensionφ:Q→Aut NdρLabelID
C241C6 = C3×D24φ: C6/C3C2 ⊆ Aut C24482C24:1C6144,72
C242C6 = C3×C24⋊C2φ: C6/C3C2 ⊆ Aut C24482C24:2C6144,71
C243C6 = C32×D8φ: C6/C3C2 ⊆ Aut C2472C24:3C6144,106
C244C6 = S3×C24φ: C6/C3C2 ⊆ Aut C24482C24:4C6144,69
C245C6 = C3×C8⋊S3φ: C6/C3C2 ⊆ Aut C24482C24:5C6144,70
C246C6 = C32×SD16φ: C6/C3C2 ⊆ Aut C2472C24:6C6144,107
C247C6 = C32×M4(2)φ: C6/C3C2 ⊆ Aut C2472C24:7C6144,105

Non-split extensions G=N.Q with N=C24 and Q=C6
extensionφ:Q→Aut NdρLabelID
C24.1C6 = C3×Dic12φ: C6/C3C2 ⊆ Aut C24482C24.1C6144,73
C24.2C6 = C9×D8φ: C6/C3C2 ⊆ Aut C24722C24.2C6144,25
C24.3C6 = C9×Q16φ: C6/C3C2 ⊆ Aut C241442C24.3C6144,27
C24.4C6 = C32×Q16φ: C6/C3C2 ⊆ Aut C24144C24.4C6144,108
C24.5C6 = C3×C3⋊C16φ: C6/C3C2 ⊆ Aut C24482C24.5C6144,28
C24.6C6 = C9×SD16φ: C6/C3C2 ⊆ Aut C24722C24.6C6144,26
C24.7C6 = C9×M4(2)φ: C6/C3C2 ⊆ Aut C24722C24.7C6144,24

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