Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 112 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. #17987405 | C3 | semidirect |
| 3. #17987338 | C3 | semidirect |
| 4. #17987336 | C3 | semidirect |
| 6. C19×#6887 | C3 | semidirect |
| 14. C3×C9×C19⋊C3 | C9 | semidirect |
| 49. #6887 | C19⋊C3 | semidirect |
| 114. C19 | #10624688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C19⋊C3 | 3 |
| #17987405 | 3 |
| #17987338 | 3 |
| #17987336 | 3 |
| #17987334 | 3 |
| C19×#6887 | 3 |
| #10624688 | 19 |