Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
788 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 328 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. #17987467 | C3 | direct (N × H) |
| 3. C3×#13095307 | C3 | semidirect |
| 4. C3×#13095306 | C3 | semidirect |
| 5. C3×#13095305 | C3 | semidirect |
| 7. C3×C9×#4294 | C3 | semidirect |
| 8. C3×C19×C9⋊C9 | C3 | semidirect |
| 16. #13095307 | C32 | semidirect |
| 17. #13095306 | C32 | semidirect |
| 18. #13095305 | C32 | semidirect |
| 20. C9×#4294 | C32 | semidirect |
| 23. C19×C9⋊C9 | C32 | semidirect |
| 47. C3×C9⋊C9 | C19⋊C3 | semidirect |
| 74. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 77. C3×C19 | #6899 | semidirect |
| 98. C19 | C3×#6899 | semidirect |
| 112. C3 | #17987467 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587023 | 3 |
| #17987467 | 3 |
| C3×#13095307 | 3 |
| C3×#13095306 | 3 |
| C3×#13095305 | 3 |
| C3×#13095303 | 3 |
| C3×C9×#4294 | 3 |
| C3×C19×C9⋊C9 | 3 |
| C3×#6899 | 19 |