Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
758 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 301 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. #17987468 | C3 | semidirect |
| 2. #17987461 | C3 | semidirect |
| 3. #17987447 | C3 | semidirect |
| 4. #17987435 | C3 | semidirect |
| 6. C9×#10587025 | C3 | semidirect |
| 7. #17987405 | C3 | semidirect |
| 8. #17987405 | C3 | semidirect |
| 9. C3×C9×#4294 | C3 | semidirect |
| 43. C3×C9×C19 | 3−1+2 | semidirect |
| 76. #4294 | #737 | semidirect |
| 118. C3×C9 | #10587025 | semidirect |
| 123. C19 | #10624879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987468 | 3 |
| #17987461 | 3 |
| #17987447 | 3 |
| #17987435 | 3 |
| #17987423 | 3 |
| C9×#10587025 | 3 |
| #17987405 | 3 |
| C3×C9×#4294 | 3 |
| C3×C19×#737 | 3 |
| #10624879 | 19 |