Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
204 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 52 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. #17987445 | C3 | semidirect |
| 2. #17987438 | C3 | semidirect |
| 3. C9×#10587025 | C3 | semidirect |
| 4. C19⋊#6862 | C3 | semidirect |
| 5. #17987323 | C3 | semidirect |
| 8. #17987317 | C3 | semidirect |
| 9. #17987317 | C3 | semidirect |
| 10. #17987316 | C3 | semidirect |
| 11. #17987316 | C3 | semidirect |
| 149. C19 | #10624624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987445 | 3 |
| #17987438 | 3 |
| C9×#10587025 | 3 |
| C19⋊#6862 | 3 |
| #17987323 | 3 |
| #17987318 | 3 |
| #17987317 | 3 |
| #17987316 | 3 |
| #17987312 | 3 |
| C9×C19×H(3,𝔽3) | 3 |
| #10624624 | 19 |