Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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. C19⋊C3×C27⋊C3 | C3 | semidirect |
| 3. #17987341 | C3 | semidirect |
| 4. #17987340 | C3 | semidirect |
| 5. C19×#6869 | C3 | semidirect |
| 18. #13095312 | C32 | semidirect |
| 23. C19×C27⋊C3 | C32 | semidirect |
| 61. #6869 | C19⋊C3 | direct (N × H) |
| 97. C27⋊C3 | C3×C19⋊C3 | semidirect |
| 105. C19⋊C3 | #6869 | direct (N × H) |
| 138. C19 | C3×#6869 | 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 |
| C19⋊C3×C27⋊C3 | 3 |
| #17987341 | 3 |
| #17987340 | 3 |
| C19×#6869 | 3 |
| C3×#6869 | 19 |