Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
926 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 454 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 |
|---|---|---|
| 2. #17987415 | C3 | semidirect |
| 3. #17987415 | C3 | semidirect |
| 4. C9×#10587025 | C3 | semidirect |
| 7. #17987402 | C3 | semidirect |
| 8. C3×#13095305 | C3 | semidirect |
| 10. #13095331 | C9 | semidirect |
| 33. #10587025 | C3×C9 | semidirect |
| 36. C3×#4294 | C3×C9 | semidirect |
| 102. C19 | #10624864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095331 | 3 |
| #17987415 | 3 |
| C9×#10587025 | 3 |
| H(3,𝔽3)×#4294 | 3 |
| #17987402 | 3 |
| C3×#13095305 | 3 |
| C9×C19×H(3,𝔽3) | 3 |
| #10624864 | 19 |