Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
416 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 87 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. (C19⋊C3)⋊(C27⋊C3) | C3 | semidirect |
| 2. #17987563 | C3 | semidirect |
| 3. #17987562 | C3 | semidirect |
| 4. #17987561 | C3 | semidirect |
| 8. #13095342 | C32 | semidirect |
| 160. C19⋊C3 | #6869 | semidirect |
| 221. C19 | C3×#6869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C19⋊C3)⋊(C27⋊C3) | 3 |
| #17987563 | 3 |
| #17987562 | 3 |
| #17987561 | 3 |
| C32×C9×C19⋊C3 | 3 |
| C3×#6869 | 19 |