Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
192 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #17987355 | C3 | semidirect |
| 4. #17987355 | C3 | semidirect |
| 5. #17987355 | C3 | semidirect |
| 6. #17987355 | C3 | semidirect |
| 7. #17987355 | C3 | semidirect |
| 8. #17987355 | C3 | semidirect |
| 10. #17987330 | C3 | semidirect |
| 11. #17987329 | C3 | semidirect |
| 12. C27×#4294 | C3 | semidirect |
| 63. #10587018 | 3−1+2 | semidirect |
| 95. #4294 | C27⋊C3 | semidirect |
| 150. C19 | #10624728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095312 | 3 |
| C9×#10587025 | 3 |
| #17987355 | 3 |
| C32⋊#10587018 | 3 |
| #17987330 | 3 |
| #17987329 | 3 |
| C27×#4294 | 3 |
| C19×C32⋊C27 | 3 |
| #10624728 | 19 |