Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
314 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 52 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×#13095331 | C3 | semidirect |
| 2. #17987440 | C3 | semidirect |
| 3. #17987423 | C3 | semidirect |
| 4. #17987415 | 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 |
| 167. C19 | #10624613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095331 | 3 |
| #17987440 | 3 |
| #17987423 | 3 |
| #17987415 | 3 |
| #17987322 | 3 |
| #17987318 | 3 |
| #17987316 | 3 |
| #17987312 | 3 |
| C19×#6856 | 3 |
| #10624613 | 19 |