Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
662 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 265 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. #17987460 | C3 | semidirect |
| 2. #17987457 | C3 | semidirect |
| 3. #17987452 | C3 | semidirect |
| 4. #17987446 | C3 | semidirect |
| 5. #17987445 | C3 | semidirect |
| 6. #17987435 | C3 | semidirect |
| 7. #17987435 | C3 | semidirect |
| 9. #17987415 | C3 | semidirect |
| 10. 3−1+2×#4294 | C3 | semidirect |
| 11. 3−1+2×#4294 | C3 | semidirect |
| 13. #17987402 | C3 | semidirect |
| 14. C3×C9×#4294 | C3 | semidirect |
| 177. C19 | #10624877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987460 | 3 |
| #17987457 | 3 |
| #17987452 | 3 |
| #17987446 | 3 |
| #17987445 | 3 |
| #17987435 | 3 |
| #17987423 | 3 |
| #17987415 | 3 |
| 3−1+2×#4294 | 3 |
| H(3,𝔽3)×#4294 | 3 |
| #17987402 | 3 |
| C3×C9×#4294 | 3 |
| C19×#6893 | 3 |
| #10624877 | 19 |