Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
232 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 232 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. #17987428 | C3 | semidirect |
| 2. #17987423 | C3 | semidirect |
| 3. H(3,𝔽3)×#4294 | C3 | semidirect |
| 4. #17987402 | C3 | semidirect |
| 5. #17987325 | C3 | semidirect |
| 6. #17987325 | C3 | semidirect |
| 7. #17987323 | C3 | semidirect |
| 8. #17987319 | C3 | semidirect |
| 9. #17987318 | C3 | semidirect |
| 10. #17987318 | C3 | semidirect |
| 11. #17987309 | C3 | semidirect |
| 12. #17987309 | C3 | semidirect |
| 13. C19×#6856 | C3 | semidirect |
| 75. #6856 | C19⋊C3 | semidirect |
| 161. C19 | #10624601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987428 | 3 |
| #17987423 | 3 |
| H(3,𝔽3)×#4294 | 3 |
| #17987402 | 3 |
| #17987325 | 3 |
| #17987323 | 3 |
| #17987319 | 3 |
| #17987318 | 3 |
| #17987309 | 3 |
| C19×#6856 | 3 |
| #10624601 | 19 |