Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
214 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 214 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. #17987431 | C3 | semidirect |
| 2. C9×#10587025 | C3 | semidirect |
| 3. #17987322 | C3 | semidirect |
| 4. #17987319 | C3 | semidirect |
| 5. #17987315 | C3 | semidirect |
| 6. #17987313 | C3 | semidirect |
| 7. #17987312 | C3 | semidirect |
| 9. C19×C9⋊H(3,𝔽3) | C3 | semidirect |
| 45. C9⋊H(3,𝔽3) | C19⋊C3 | semidirect |
| 110. C19 | #10624627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987431 | 3 |
| C9×#10587025 | 3 |
| #17987322 | 3 |
| #17987319 | 3 |
| #17987315 | 3 |
| #17987313 | 3 |
| #17987312 | 3 |
| #17987309 | 3 |
| C19×C9⋊H(3,𝔽3) | 3 |
| #10624627 | 19 |