Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
216 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 66 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. #17987599 | C3 | semidirect |
| 2. #17987598 | C3 | semidirect |
| 3. C3×#13095343 | C3 | semidirect |
| 4. #17987569 | C3 | semidirect |
| 5. #17987568 | C3 | semidirect |
| 6. #17987567 | C3 | semidirect |
| 7. #17987566 | C3 | semidirect |
| 8. #17987563 | C3 | semidirect |
| 127. C19 | #10624725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987599 | 3 |
| #17987598 | 3 |
| C3×#13095343 | 3 |
| #17987569 | 3 |
| #17987568 | 3 |
| #17987567 | 3 |
| #17987566 | 3 |
| #17987563 | 3 |
| #17987499 | 3 |
| #10624725 | 19 |