Finite Group DatabasebetaFinite Group DatabasebetaOrder 33777.
110 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 47 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. #26014604 | C3 | semidirect |
| 3. #26014603 | C3 | semidirect |
| 4. (C139⋊C9)⋊C9 | C3 | semidirect |
| 5. (C139⋊C9)⋊C9 | C3 | semidirect |
| 6. (C139⋊C9)⋊C9 | C3 | semidirect |
| 7. (C139⋊C9)⋊C9 | C3 | semidirect |
| 8. (C139⋊C9)⋊C9 | C3 | semidirect |
| 9. (C139⋊C9)⋊C9 | C3 | semidirect |
| 12. C9×C139⋊C9 | C3 | semidirect |
| 51. C139 | #6899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16836730 | 3 |
| #26014604 | 3 |
| #26014603 | 3 |
| (C139⋊C9)⋊C9 | 3 |
| C32⋊(C139⋊C9) | 3 |
| C9×C139⋊C9 | 3 |
| C32⋊C9×C139 | 3 |
| #6899 | 139 |