Template:Groups of order 36 automorphism groups
| Group | Second part of GAP ID | Isomorphism class of automorphism group | Automorphism group order |
|---|---|---|---|
| Dicyclic group:Dic36 | 1 | Direct product of Z2 and SmallGroup(54,6) | 108 |
| Cyclic group:Z36 | 2 | Direct product of Z6 and Z2 | 12 |
| SmallGroup(36,3) | 3 | Direct product of S4 and Z3 | 72 |
| Dihedral group:D36 | 4 | Direct product of Z2 and SmallGroup(54,6) | 108 |
| Direct product of E4 and Z9 | 5 | Direct product of D12 and Z3 | 36 |
| SmallGroup(36,6) | 6 | Direct product of D12 and Z2 | 24 |
| SmallGroup(36,7) | 7 | Direct product of Z2 and GA(2,3) | 864 |
| Direct product of E9 and Z4 | 8 | Direct product of Z2 and GL(2,3) | 96 |
| SmallGroup(36,9) | 9 | General semiaffine group:GammaA(1,9) | 144 |
| Direct product of S3 and S3 | 10 | Wreath product of S3 and Z2 | 72 |
| Direct product of A4 and Z3 | 11 | Direct product of S3 and S4 | 144 |
| SmallGroup(36,12) | 12 | Direct product of D12 and Z2 | 24 |
| SmallGroup(36,13) | 13 | Direct product of Z2 and GA(2,3) | 864 |
| Direct product of E4 and E9 | 14 | Direct product of S3 and GL(2,3) | 288 |