Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
980 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 268 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17987547 | C3 | semidirect |
| 2. #17987546 | C3 | semidirect |
| 3. C32×#10587025 | C3 | semidirect |
| 4. #17987521 | C3 | semidirect |
| 5. #17987520 | C3 | semidirect |
| 6. #17987518 | C3 | semidirect |
| 7. #17987514 | C3 | semidirect |
| 8. #17987511 | C3 | semidirect |
| 9. #17987509 | C3 | semidirect |
| 10. #17987496 | C3 | semidirect |
| 11. C3×#13095314 | C3 | semidirect |
| 12. C3×C19×AΣL(1,𝔽27) | C3 | semidirect |
| 14. #13095333 | C32 | semidirect |
| 17. #13095331 | C32 | semidirect |
| 26. C3×#10587025 | C32 | semidirect |
| 27. C3×#10587025 | C32 | semidirect |
| 30. C32×#4294 | C32 | semidirect |
| 31. #13095321 | C32 | semidirect |
| 32. #13095319 | C32 | semidirect |
| 33. #13095318 | C32 | semidirect |
| 34. #13095316 | C32 | semidirect |
| 35. #13095314 | C32 | semidirect |
| 36. #13095314 | C32 | semidirect |
| 37. #13095314 | C32 | semidirect |
| 41. C19×AΣL(1,𝔽27) | C32 | semidirect |
| 42. C19×AΣL(1,𝔽27) | C32 | semidirect |
| 43. C19×AΣL(1,𝔽27) | C32 | semidirect |
| 99. C3×AΣL(1,𝔽27) | C19⋊C3 | semidirect |
| 150. AΣL(1,𝔽27) | C3×C19⋊C3 | semidirect |
| 151. AΣL(1,𝔽27) | C3×C19⋊C3 | semidirect |
| 152. AΣL(1,𝔽27) | C3×C19⋊C3 | semidirect |
| 205. C19 | #10624934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987547 | 3 |
| #17987546 | 3 |
| C32×#10587025 | 3 |
| #17987521 | 3 |
| #17987520 | 3 |
| #17987518 | 3 |
| #17987514 | 3 |
| #17987511 | 3 |
| #17987509 | 3 |
| #17987496 | 3 |
| C3×#13095314 | 3 |
| C3×C19×AΣL(1,𝔽27) | 3 |
| #10624934 | 19 |