Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
488 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 488 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. #17987546 | C3 | semidirect |
| 2. #17987514 | C3 | semidirect |
| 3. #17987511 | C3 | semidirect |
| 4. #17987511 | C3 | semidirect |
| 5. #17987510 | C3 | semidirect |
| 6. #17987506 | C3 | semidirect |
| 7. #17987506 | C3 | semidirect |
| 8. #17987505 | C3 | semidirect |
| 9. #17987504 | C3 | semidirect |
| 10. C3×#13095314 | C3 | semidirect |
| 11. #17987421 | C3 | semidirect |
| 12. #17987417 | C3 | semidirect |
| 13. C3×C19×AΣL(1,𝔽27) | C3 | semidirect |
| 60. C19×3−1+2 | H(3,𝔽3) | semidirect |
| 93. #10587025 | H(3,𝔽3) | semidirect |
| 98. C3×#4294 | H(3,𝔽3) | semidirect |
| 112. C3×AΣL(1,𝔽27) | C19⋊C3 | semidirect |
| 217. 3−1+2 | C32⋊(C19⋊C3) | semidirect |
| 242. C19 | #10624749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987546 | 3 |
| #17987514 | 3 |
| #17987511 | 3 |
| #17987510 | 3 |
| #17987506 | 3 |
| #17987505 | 3 |
| #17987504 | 3 |
| C3×#13095314 | 3 |
| #17987421 | 3 |
| #17987417 | 3 |
| C3×C19×AΣL(1,𝔽27) | 3 |
| #10624749 | 19 |