Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
446 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 61 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. #17987547 | C3 | semidirect |
| 2. #17987519 | C3 | semidirect |
| 3. #17987518 | C3 | semidirect |
| 4. #17987511 | C3 | semidirect |
| 5. #17987509 | C3 | semidirect |
| 6. #17987504 | C3 | semidirect |
| 7. C3×#13095314 | C3 | semidirect |
| 8. #17987421 | C3 | semidirect |
| 9. C3×C19×AΣL(1,𝔽27) | C3 | semidirect |
| 73. C3×AΣL(1,𝔽27) | C19⋊C3 | semidirect |
| 156. C19 | #10624752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987547 | 3 |
| #17987519 | 3 |
| #17987518 | 3 |
| #17987511 | 3 |
| #17987509 | 3 |
| #17987504 | 3 |
| C3×#13095314 | 3 |
| #17987421 | 3 |
| C3×C19×AΣL(1,𝔽27) | 3 |
| #10624752 | 19 |