Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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. #17987441 | C3 | semidirect |
| 2. #17987429 | C3 | semidirect |
| 3. #17987415 | C3 | semidirect |
| 4. H(3,𝔽3)×#4294 | C3 | semidirect |
| 5. #17987322 | C3 | semidirect |
| 6. #17987322 | C3 | semidirect |
| 7. #17987318 | C3 | semidirect |
| 8. #17987316 | C3 | semidirect |
| 9. #17987316 | C3 | semidirect |
| 10. #17987312 | C3 | semidirect |
| 11. #17987312 | C3 | semidirect |
| 12. #17987312 | C3 | semidirect |
| 159. C19 | #10624623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987441 | 3 |
| #17987429 | 3 |
| #17987415 | 3 |
| H(3,𝔽3)×#4294 | 3 |
| #17987322 | 3 |
| #17987318 | 3 |
| #17987316 | 3 |
| #17987312 | 3 |
| C19×#6856 | 3 |
| #10624623 | 19 |