Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
222 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 1. C3×#13095320 | C3 | semidirect |
| 2. #17987405 | C3 | semidirect |
| 3. #17987373 | C3 | semidirect |
| 4. C3×C19×#732 | C3 | semidirect |
| 8. #13095320 | C32 | semidirect |
| 12. C9×#4294 | C32 | semidirect |
| 17. C19×#732 | C32 | semidirect |
| 34. C3×#732 | C19⋊C3 | semidirect |
| 57. #732 | C3×C19⋊C3 | semidirect |
| 82. C19 | #10624839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095320 | 3 |
| #17987405 | 3 |
| #17987373 | 3 |
| C3×C19×#732 | 3 |
| #10624839 | 19 |