Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
764 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 256 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. #17987431 | C3 | semidirect |
| 2. #17987430 | C3 | semidirect |
| 3. #17987428 | C3 | semidirect |
| 4. #17987427 | C3 | semidirect |
| 5. #17987426 | C3 | semidirect |
| 6. #17987425 | C3 | semidirect |
| 7. #17987424 | C3 | semidirect |
| 8. #17987424 | C3 | semidirect |
| 9. #17987423 | C3 | semidirect |
| 10. #17987420 | C3 | semidirect |
| 11. #17987419 | C3 | semidirect |
| 13. C9×C32⋊(C19⋊C3) | C3 | semidirect |
| 14. C3×#13095303 | C3 | semidirect |
| 15. C9×C19×H(3,𝔽3) | C3 | semidirect |
| 17. C3×#10587025 | C32 | semidirect |
| 19. C3×#10587022 | C32 | semidirect |
| 21. C3×#10587023 | C32 | semidirect |
| 27. C3×C9×C19⋊C3 | C32 | semidirect |
| 30. C32⋊#4294 | C32 | semidirect |
| 31. C32⋊#4294 | C32 | semidirect |
| 42. #13095303 | C32 | semidirect |
| 43. #13095303 | C32 | semidirect |
| 44. #13095303 | C32 | semidirect |
| 45. #13095303 | C32 | semidirect |
| 46. #13095303 | C32 | semidirect |
| 47. #13095303 | C32 | semidirect |
| 50. C32×C9×C19 | C32 | semidirect |
| 53. C19×C32⋊C9 | C32 | semidirect |
| 101. C9×H(3,𝔽3) | C19⋊C3 | semidirect |
| 152. C32×C9 | C3×C19⋊C3 | semidirect |
| 175. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 219. C19 | #10624888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987431 | 3 |
| #17987430 | 3 |
| #17987428 | 3 |
| #17987427 | 3 |
| #17987426 | 3 |
| #17987425 | 3 |
| #17987424 | 3 |
| #17987423 | 3 |
| #17987420 | 3 |
| #17987419 | 3 |
| (C3×C19⋊C3)⋊H(3,𝔽3) | 3 |
| C9×C32⋊(C19⋊C3) | 3 |
| C3×#13095303 | 3 |
| C9×C19×H(3,𝔽3) | 3 |
| #10624888 | 19 |