Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
992 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 274 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. C3×#13095333 | C3 | semidirect |
| 2. C3×#13095331 | C3 | semidirect |
| 3. C32×#10587025 | C3 | semidirect |
| 4. #17987521 | C3 | direct (N × H) |
| 5. C3×#13095321 | C3 | semidirect |
| 6. C3×#13095319 | C3 | semidirect |
| 7. C3×#13095318 | C3 | semidirect |
| 8. C3×#13095316 | C3 | semidirect |
| 9. C3×#13095314 | C3 | semidirect |
| 10. C3×C19×AΣL(1,𝔽27) | C3 | semidirect |
| 12. #13095333 | C32 | semidirect |
| 14. #13095331 | C32 | semidirect |
| 21. C3×#10587025 | C32 | semidirect |
| 30. #13095321 | C32 | semidirect |
| 31. #13095319 | C32 | semidirect |
| 32. #13095318 | C32 | semidirect |
| 33. #13095316 | C32 | semidirect |
| 34. #13095314 | C32 | semidirect |
| 38. C19×AΣL(1,𝔽27) | C32 | semidirect |
| 86. C3×AΣL(1,𝔽27) | C19⋊C3 | semidirect |
| 133. AΣL(1,𝔽27) | C3×C19⋊C3 | semidirect |
| 138. C3×C19 | #6913 | semidirect |
| 178. C19 | C3×#6913 | semidirect |
| 203. C3 | #17987521 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095333 | 3 |
| C3×#13095331 | 3 |
| C32×#10587025 | 3 |
| #17987521 | 3 |
| C3×#13095321 | 3 |
| C3×#13095319 | 3 |
| C3×#13095318 | 3 |
| C3×#13095316 | 3 |
| C3×#13095314 | 3 |
| C3×C19×AΣL(1,𝔽27) | 3 |
| C3×#6913 | 19 |