Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1076 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 1076 conjugacy classes of subgroups — too many to draw. Only its 382 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. #17987468 | C3 | direct (N × H) |
| 3. C3×#13095307 | C3 | semidirect |
| 4. C3×#13095306 | C3 | semidirect |
| 5. C3×#13095305 | C3 | semidirect |
| 6. C3×C9×#4294 | C3 | semidirect |
| 13. #13095307 | C32 | semidirect |
| 14. #13095306 | C32 | semidirect |
| 15. #13095305 | C32 | semidirect |
| 16. C9×#4294 | C32 | semidirect |
| 29. C3×C9×C19 | 3−1+2 | semidirect |
| 35. C3×#4294 | 3−1+2 | semidirect |
| 53. C9×C19 | C3×3−1+2 | semidirect |
| 56. #4294 | C3×3−1+2 | semidirect |
| 72. C3×C19 | #6900 | semidirect |
| 88. C3×C9 | #10587025 | semidirect |
| 91. C19 | C3×#6900 | semidirect |
| 102. C9 | C3×#10587025 | semidirect |
| 104. C3 | #17987468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587025 | 3 |
| #17987468 | 3 |
| C3×#13095307 | 3 |
| C3×#13095306 | 3 |
| C3×#13095305 | 3 |
| C3×C9×#4294 | 3 |
| C32×C19×3−1+2 | 3 |
| C3×#6900 | 19 |