Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
314 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 58 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. #17987439 | C3 | semidirect |
| 2. #17987425 | C3 | semidirect |
| 3. C9×#10587025 | C3 | semidirect |
| 4. #17987321 | C3 | semidirect |
| 5. #17987321 | C3 | semidirect |
| 6. #17987318 | C3 | semidirect |
| 7. #17987314 | C3 | semidirect |
| 8. #17987314 | C3 | semidirect |
| 9. #17987312 | C3 | semidirect |
| 10. #17987311 | C3 | semidirect |
| 11. #17987311 | C3 | semidirect |
| 13. C3×C19×#737 | C3 | semidirect |
| 68. C3×#737 | C19⋊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 |
|---|---|
| #17987439 | 3 |
| #17987425 | 3 |
| C9×#10587025 | 3 |
| #17987321 | 3 |
| #17987318 | 3 |
| #17987314 | 3 |
| #17987312 | 3 |
| #17987311 | 3 |
| #17987309 | 3 |
| C3×C19×#737 | 3 |
| #10624613 | 19 |