Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
936 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 268 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 |
|---|---|---|
| 3. #17987519 | C3 | semidirect |
| 4. #17987518 | C3 | semidirect |
| 5. #17987517 | C3 | semidirect |
| 6. #17987516 | C3 | semidirect |
| 7. C3×#13095321 | C3 | semidirect |
| 8. C19⋊C3×#733 | C3 | semidirect |
| 9. C19×#6912 | C3 | semidirect |
| 60. #6912 | C19⋊C3 | semidirect |
| 122. C19 | #10624933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987546 | 3 |
| C3×#13095333 | 3 |
| #17987519 | 3 |
| #17987518 | 3 |
| #17987517 | 3 |
| #17987516 | 3 |
| C3×#13095321 | 3 |
| C19⋊C3×#733 | 3 |
| C19×#6912 | 3 |
| #10624933 | 19 |