Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
926 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 454 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. C9×#10587025 | C3 | semidirect |
| 3. #17987410 | C3 | semidirect |
| 4. #17987409 | C3 | semidirect |
| 6. #17987405 | C3 | semidirect |
| 7. #17987405 | C3 | semidirect |
| 8. #17987404 | C3 | semidirect |
| 9. C19⋊C3×C9⋊C9 | C3 | semidirect |
| 10. C3×C19×C9⋊C9 | C3 | semidirect |
| 11. #13095332 | C9 | semidirect |
| 40. C3×C9×C19 | C3×C9 | semidirect |
| 47. #10587025 | C3×C9 | semidirect |
| 51. #10587023 | C3×C9 | semidirect |
| 52. #10587022 | C3×C9 | semidirect |
| 54. C9×C19⋊C3 | C3×C9 | semidirect |
| 64. C3×C9⋊C9 | C19⋊C3 | semidirect |
| 119. C3×C9 | C9×C19⋊C3 | semidirect |
| 125. C19 | #10624864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095332 | 3 |
| C9×#10587025 | 3 |
| #17987410 | 3 |
| #17987409 | 3 |
| C9×C32⋊(C19⋊C3) | 3 |
| #17987405 | 3 |
| #17987404 | 3 |
| C19⋊C3×C9⋊C9 | 3 |
| C3×C19×C9⋊C9 | 3 |
| #10624864 | 19 |