Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
198 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 4. #17987578 | C3 | semidirect |
| 5. #17987576 | C3 | semidirect |
| 6. #17987574 | C3 | semidirect |
| 23. #13095312 | C9 | semidirect |
| 25. #13095310 | C9 | semidirect |
| 26. C27×C19⋊C3 | C9 | semidirect |
| 27. C19×C27⋊C3 | C9 | semidirect |
| 83. C27⋊C3 | #4296 | semidirect |
| 116. C19 | #10624709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095343 | 3 |
| (C19⋊C3)⋊(C27⋊C3) | 3 |
| #17987589 | 3 |
| #17987578 | 3 |
| #17987576 | 3 |
| #17987574 | 3 |
| C19⋊C3×C27⋊C3 | 3 |
| #10624709 | 19 |