Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
414 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 70 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. #17987518 | C3 | semidirect |
| 2. #17987514 | C3 | semidirect |
| 3. #17987511 | C3 | semidirect |
| 4. #17987509 | C3 | semidirect |
| 5. #17987506 | C3 | semidirect |
| 6. #17987504 | C3 | semidirect |
| 7. C3×#13095317 | C3 | semidirect |
| 8. C3×#13095317 | C3 | semidirect |
| 9. C3×C19×#737 | C3 | semidirect |
| 69. C3×#737 | C19⋊C3 | semidirect |
| 160. C19 | #10624756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987518 | 3 |
| #17987514 | 3 |
| #17987511 | 3 |
| #17987509 | 3 |
| #17987506 | 3 |
| #17987504 | 3 |
| C3×#13095317 | 3 |
| C3×C19×#737 | 3 |
| #10624756 | 19 |