Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
698 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 292 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 |
|---|---|---|
| 2. #17987470 | C3 | semidirect |
| 3. #17987462 | C3 | semidirect |
| 4. #17987451 | C3 | semidirect |
| 5. #17987440 | C3 | semidirect |
| 6. #17987433 | C3 | semidirect |
| 8. #17987405 | C3 | semidirect |
| 9. C3×#13095307 | C3 | semidirect |
| 10. C19×#6887 | C3 | semidirect |
| 38. C3×C9×C19 | 3−1+2 | semidirect |
| 62. #6887 | C19⋊C3 | semidirect |
| 118. C3×C9 | #10587023 | semidirect |
| 123. C19 | #10624887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095332 | 3 |
| #17987470 | 3 |
| #17987462 | 3 |
| #17987451 | 3 |
| #17987440 | 3 |
| #17987433 | 3 |
| #17987427 | 3 |
| #17987405 | 3 |
| C3×#13095307 | 3 |
| C19×#6887 | 3 |
| #10624887 | 19 |