Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 948 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. #17987544 | C3 | semidirect |
| 2. C3×#13095332 | C3 | semidirect |
| 3. #17987529 | C3 | semidirect |
| 4. #17987524 | C3 | semidirect |
| 5. #17987523 | C3 | semidirect |
| 6. #17987521 | C3 | semidirect |
| 7. #17987516 | C3 | semidirect |
| 8. #17987512 | C3 | semidirect |
| 9. #17987503 | C3 | semidirect |
| 10. #17987500 | C3 | semidirect |
| 11. #17987499 | C3 | semidirect |
| 12. C19⋊C3×#731 | C3 | semidirect |
| 13. C19×#6908 | C3 | semidirect |
| 15. #13095333 | C32 | semidirect |
| 19. #13095332 | C32 | semidirect |
| 20. #13095331 | C32 | semidirect |
| 21. C3×#10587025 | C32 | semidirect |
| 23. C3×#10587022 | C32 | semidirect |
| 26. C3×#10587023 | C32 | semidirect |
| 32. C3×C9×C19⋊C3 | C32 | semidirect |
| 33. #13095322 | C32 | semidirect |
| 34. #13095321 | C32 | semidirect |
| 37. #13095318 | C32 | semidirect |
| 38. #13095317 | C32 | semidirect |
| 39. #13095316 | C32 | semidirect |
| 40. #13095315 | C32 | semidirect |
| 41. #13095314 | C32 | semidirect |
| 42. #13095313 | C32 | semidirect |
| 43. C19×#737 | C32 | semidirect |
| 44. C32×C9×C19 | C32 | semidirect |
| 45. C19×#733 | C32 | semidirect |
| 47. C19×#731 | C32 | semidirect |
| 48. C19×AΣL(1,𝔽27) | C32 | semidirect |
| 101. #6908 | C19⋊C3 | semidirect |
| 129. #737 | C3×C19⋊C3 | semidirect |
| 142. C32×C9 | C3×C19⋊C3 | semidirect |
| 145. #733 | C3×C19⋊C3 | semidirect |
| 152. #731 | C3×C19⋊C3 | semidirect |
| 156. AΣL(1,𝔽27) | C3×C19⋊C3 | semidirect |
| 204. C19 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987544 | 3 |
| C3×#13095332 | 3 |
| #17987529 | 3 |
| #17987524 | 3 |
| #17987523 | 3 |
| #17987521 | 3 |
| #17987516 | 3 |
| #17987512 | 3 |
| #17987503 | 3 |
| #17987500 | 3 |
| #17987499 | 3 |
| C19⋊C3×#731 | 3 |
| C19×#6908 | 3 |
| #10624935 | 19 |