Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
216 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 55 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. #17987443 | C3 | semidirect |
| 3. #17987402 | C3 | semidirect |
| 4. C3×#13095307 | C3 | semidirect |
| 5. #17987348 | C3 | semidirect |
| 6. #17987347 | C3 | semidirect |
| 7. 3−1+2⋊#4294 | C3 | semidirect |
| 8. 3−1+2⋊#4294 | C3 | semidirect |
| 9. #17987345 | C3 | semidirect |
| 13. C19×3−1+2⋊C9 | C3 | semidirect |
| 71. 3−1+2⋊C9 | C19⋊C3 | semidirect |
| 152. C19 | #10624827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987443 | 3 |
| #17987432 | 3 |
| #17987402 | 3 |
| C3×#13095307 | 3 |
| #17987348 | 3 |
| #17987347 | 3 |
| 3−1+2⋊#4294 | 3 |
| #17987345 | 3 |
| #17987344 | 3 |
| #17987342 | 3 |
| C19×3−1+2⋊C9 | 3 |
| #10624827 | 19 |