Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
960 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 286 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. C3×#13095332 | C3 | semidirect |
| 2. C3×#13095332 | C3 | semidirect |
| 3. #17987523 | C3 | semidirect |
| 4. #17987522 | C3 | semidirect |
| 5. #17987518 | C3 | semidirect |
| 6. #17987514 | C3 | semidirect |
| 7. #17987511 | C3 | semidirect |
| 8. #17987509 | C3 | semidirect |
| 9. #17987506 | C3 | semidirect |
| 10. #17987504 | C3 | semidirect |
| 11. #17987497 | C3 | semidirect |
| 12. C3×C19×#737 | C3 | semidirect |
| 24. #13095332 | C32 | semidirect |
| 25. #13095332 | C32 | semidirect |
| 26. #13095332 | C32 | semidirect |
| 32. C3×#10587022 | C32 | semidirect |
| 34. C3×#10587023 | C32 | semidirect |
| 38. C3×C9×C19⋊C3 | C32 | semidirect |
| 39. #13095321 | C32 | semidirect |
| 41. #13095318 | C32 | semidirect |
| 42. #13095316 | C32 | semidirect |
| 43. #13095315 | C32 | semidirect |
| 44. #13095313 | C32 | semidirect |
| 48. C19×#737 | C32 | semidirect |
| 49. C19×#737 | C32 | semidirect |
| 50. C19×#737 | C32 | semidirect |
| 116. C3×#737 | C19⋊C3 | semidirect |
| 164. #737 | C3×C19⋊C3 | semidirect |
| 165. #737 | C3×C19⋊C3 | semidirect |
| 166. #737 | C3×C19⋊C3 | semidirect |
| 254. C19 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095332 | 3 |
| #17987523 | 3 |
| #17987522 | 3 |
| #17987518 | 3 |
| #17987514 | 3 |
| #17987511 | 3 |
| #17987509 | 3 |
| #17987506 | 3 |
| #17987504 | 3 |
| #17987497 | 3 |
| C3×C19×#737 | 3 |
| #10624929 | 19 |