Finite Group DatabasebetaFinite Group DatabasebetaOrder 33777.
100 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 44 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. #26014604 | C3 | semidirect |
| 2. #26014603 | C3 | semidirect |
| 3. (C139⋊C9)⋊C9 | 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 |
| 12. C9×C139⋊C9 | C3 | semidirect |
| 13. C9⋊C9×C139 | C3 | semidirect |
| 50. C139 | #6897 | semidirect |
| 58. C9⋊C9 | C139⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26014604 | 3 |
| #26014603 | 3 |
| (C139⋊C9)⋊C9 | 3 |
| (C3×C139⋊C3)⋊C9 | 3 |
| C9×C139⋊C9 | 3 |
| C9⋊C9×C139 | 3 |
| #6897 | 139 |