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. #17987544 | C3 | semidirect |
| 2. C32×#10587023 | C3 | semidirect |
| 3. #17987530 | C3 | semidirect |
| 4. #17987526 | C3 | semidirect |
| 5. #17987525 | C3 | semidirect |
| 6. #17987523 | C3 | semidirect |
| 7. #17987517 | C3 | semidirect |
| 8. #17987513 | C3 | semidirect |
| 9. #17987507 | C3 | semidirect |
| 10. #17987500 | C3 | semidirect |
| 11. #17987496 | C3 | semidirect |
| 12. C19⋊C3×AΣL(1,𝔽27) | C3 | semidirect |
| 13. C19×#6908 | C3 | semidirect |
| 16. #13095333 | C32 | semidirect |
| 18. #13095332 | C32 | semidirect |
| 19. #13095331 | C32 | semidirect |
| 26. C3×#10587023 | C32 | semidirect |
| 27. C3×#10587023 | C32 | semidirect |
| 28. C3×#10587023 | C32 | semidirect |
| 32. C32×#4294 | C32 | semidirect |
| 33. #13095322 | C32 | semidirect |
| 34. #13095321 | C32 | semidirect |
| 35. #13095320 | C32 | semidirect |
| 36. #13095319 | 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 |
| 46. C19×#732 | C32 | semidirect |
| 47. C19×#731 | C32 | semidirect |
| 48. C19×AΣL(1,𝔽27) | C32 | semidirect |
| 102. #6908 | C19⋊C3 | semidirect |
| 130. #737 | C3×C19⋊C3 | semidirect |
| 144. C32×C9 | C3×C19⋊C3 | semidirect |
| 147. #733 | C3×C19⋊C3 | semidirect |
| 150. #732 | C3×C19⋊C3 | semidirect |
| 154. #731 | C3×C19⋊C3 | semidirect |
| 158. AΣL(1,𝔽27) | C3×C19⋊C3 | semidirect |
| 207. C19 | #10624934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987544 | 3 |
| C32×#10587023 | 3 |
| #17987530 | 3 |
| #17987526 | 3 |
| #17987525 | 3 |
| #17987523 | 3 |
| #17987517 | 3 |
| #17987513 | 3 |
| #17987507 | 3 |
| #17987500 | 3 |
| #17987496 | 3 |
| C19⋊C3×AΣL(1,𝔽27) | 3 |
| C19×#6908 | 3 |
| #10624934 | 19 |