Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
758 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 310 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. #17987448 | C3 | semidirect |
| 5. #17987439 | C3 | semidirect |
| 7. C9×#10587023 | C3 | semidirect |
| 8. #17987405 | C3 | semidirect |
| 9. C3×C92×C19 | C3 | semidirect |
| 34. C3×C9×C19 | 3−1+2 | semidirect |
| 56. C3×C92 | C19⋊C3 | semidirect |
| 66. C9×C19 | #737 | semidirect |
| 104. C3×C9 | #10587023 | semidirect |
| 110. C19 | #10624879 | semidirect |
| 122. C9 | #13095332 | 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 |
| #17987448 | 3 |
| #17987439 | 3 |
| #17987426 | 3 |
| C9×#10587023 | 3 |
| #17987405 | 3 |
| C3×C92×C19 | 3 |
| #10624879 | 19 |