Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
944 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 944 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. #17987415 | C3 | semidirect |
| 3. C9×#10587025 | C3 | semidirect |
| 4. #17987402 | C3 | semidirect |
| 7. C3×#10587025 | C9 | semidirect |
| 12. #13095305 | C32 | semidirect |
| 16. C9×#4294 | C32 | semidirect |
| 30. #10587025 | C3×C9 | semidirect |
| 31. #10587025 | C3×C9 | semidirect |
| 33. C3×#4294 | C3×C9 | semidirect |
| 91. C19 | #10624863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587025 | 3 |
| #17987415 | 3 |
| C9×#10587025 | 3 |
| #17987402 | 3 |
| C3×C32⋊#4294 | 3 |
| C3×C19×C32⋊C9 | 3 |
| #10624863 | 19 |