Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
220 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #17987356 | C3 | semidirect |
| 4. #17987355 | C3 | semidirect |
| 5. #17987355 | C3 | semidirect |
| 7. C9×#10587018 | C3 | semidirect |
| 8. C27×#4294 | C3 | semidirect |
| 9. C19×C9⋊C27 | C3 | semidirect |
| 32. #10587023 | C27 | semidirect |
| 40. #10587018 | 3−1+2 | semidirect |
| 46. C9⋊C27 | C19⋊C3 | semidirect |
| 55. C9×C19 | C3×C27 | semidirect |
| 60. #4294 | C3×C27 | semidirect |
| 95. C19 | C27×3−1+2 | semidirect |
| 104. C9 | C27×C19⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C27×C19⋊C3 | 3 |
| C9×#10587023 | 3 |
| #17987356 | 3 |
| #17987355 | 3 |
| #17987332 | 3 |
| C9×#10587018 | 3 |
| C27×#4294 | 3 |
| C19×C9⋊C27 | 3 |
| C27×3−1+2 | 19 |