Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
290 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 144 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. #17987555 | C3 | semidirect |
| 5. C9×#10587020 | C3 | semidirect |
| 7. #13095344 | C9 | semidirect |
| 8. #13095343 | C9 | semidirect |
| 9. (C19⋊C3)⋊C27 | C9 | semidirect |
| 84. C19 | #10624681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095344 | 3 |
| C3×#13095343 | 3 |
| C3×(C19⋊C3)⋊C27 | 3 |
| #17987555 | 3 |
| C9×#10587020 | 3 |
| #17987404 | 3 |
| #10624681 | 19 |