Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 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. #17987425 | C3 | semidirect |
| 2. #17987405 | C3 | semidirect |
| 3. #17987325 | C3 | semidirect |
| 4. #17987324 | C3 | semidirect |
| 5. #17987320 | C3 | semidirect |
| 6. #17987318 | C3 | semidirect |
| 7. #17987310 | C3 | semidirect |
| 8. #17987309 | C3 | semidirect |
| 9. C9×C19×H(3,𝔽3) | C3 | semidirect |
| 47. C9×H(3,𝔽3) | C19⋊C3 | semidirect |
| 116. C19 | #10624601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987425 | 3 |
| #17987405 | 3 |
| #17987325 | 3 |
| #17987324 | 3 |
| #17987320 | 3 |
| #17987318 | 3 |
| #17987310 | 3 |
| #17987309 | 3 |
| C9×C19×H(3,𝔽3) | 3 |
| #10624601 | 19 |