Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1328 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 328 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. C32×#10587025 | C3 | semidirect |
| 2. C32×#10587022 | C3 | semidirect |
| 3. C32×#10587023 | C3 | semidirect |
| 5. C32×C9×C19⋊C3 | C3 | semidirect |
| 6. #17987424 | C3 | direct (N × H) |
| 7. C3×C32⋊#4294 | C3 | semidirect |
| 8. C3×#13095303 | C3 | semidirect |
| 9. C3×#13095303 | C3 | semidirect |
| 10. C3×#13095303 | C3 | semidirect |
| 11. C3×#13095303 | C3 | semidirect |
| 12. C3×#13095303 | C3 | semidirect |
| 13. C3×#13095303 | C3 | semidirect |
| 14. C3×C19×C32⋊C9 | C3 | semidirect |
| 19. C3×#10587025 | C32 | semidirect |
| 21. C3×#10587022 | C32 | semidirect |
| 23. C3×#10587023 | C32 | semidirect |
| 33. C3×C9×C19⋊C3 | C32 | semidirect |
| 34. C32⋊#4294 | C32 | semidirect |
| 35. #13095303 | C32 | semidirect |
| 36. #13095303 | C32 | semidirect |
| 37. #13095303 | C32 | semidirect |
| 38. #13095303 | C32 | semidirect |
| 39. #13095303 | C32 | semidirect |
| 40. #13095303 | C32 | semidirect |
| 45. C19×C32⋊C9 | C32 | semidirect |
| 64. C32×C19⋊C3 | 3−1+2 | semidirect |
| 81. C3×#4294 | H(3,𝔽3) | semidirect |
| 104. C3×C32⋊C9 | C19⋊C3 | semidirect |
| 129. C3×C19⋊C3 | C3×3−1+2 | semidirect |
| 138. #4294 | C3×H(3,𝔽3) | semidirect |
| 169. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 171. C3×C19 | C9⋊H(3,𝔽3) | semidirect |
| 223. C19 | C3×C9⋊H(3,𝔽3) | semidirect |
| 262. C3 | #17987424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587025 | 3 |
| C32×#10587022 | 3 |
| C32×#10587023 | 3 |
| C32×C32⋊(C19⋊C3) | 3 |
| C32×C9×C19⋊C3 | 3 |
| #17987424 | 3 |
| C3×C32⋊#4294 | 3 |
| C3×#13095303 | 3 |
| C3×C19×C32⋊C9 | 3 |
| C3×C9⋊H(3,𝔽3) | 19 |