Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1328 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 346 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×#10587022 | C3 | semidirect |
| 2. C32×#10587023 | C3 | semidirect |
| 4. C32×C9×C19⋊C3 | C3 | semidirect |
| 5. #17987422 | C3 | direct (N × H) |
| 6. C3×C32⋊#4294 | C3 | semidirect |
| 7. C3×#13095303 | C3 | semidirect |
| 8. C3×#13095303 | C3 | semidirect |
| 9. C3×#13095303 | C3 | semidirect |
| 10. C32×C19×3−1+2 | C3 | semidirect |
| 15. C3×#10587022 | C32 | semidirect |
| 17. C3×#10587023 | C32 | semidirect |
| 24. C3×C9×C19⋊C3 | C32 | semidirect |
| 25. C32⋊#4294 | C32 | semidirect |
| 26. #13095303 | C32 | semidirect |
| 27. #13095303 | C32 | semidirect |
| 28. #13095303 | C32 | semidirect |
| 31. C3×C19×3−1+2 | C32 | semidirect |
| 48. C32×C19⋊C3 | 3−1+2 | semidirect |
| 54. C3×C9×C19 | H(3,𝔽3) | semidirect |
| 69. C32×3−1+2 | C19⋊C3 | semidirect |
| 96. C3×C19⋊C3 | C3×3−1+2 | semidirect |
| 98. C9×C19 | C3×H(3,𝔽3) | semidirect |
| 111. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 126. C3×C19 | C9⋊H(3,𝔽3) | semidirect |
| 162. C3×C9 | C32⋊(C19⋊C3) | semidirect |
| 165. C19 | C3×C9⋊H(3,𝔽3) | semidirect |
| 190. C9 | C3×C32⋊(C19⋊C3) | semidirect |
| 195. C3 | #17987422 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587022 | 3 |
| C32×#10587023 | 3 |
| C32×C32⋊(C19⋊C3) | 3 |
| C32×C9×C19⋊C3 | 3 |
| #17987422 | 3 |
| C3×C32⋊#4294 | 3 |
| C3×#13095303 | 3 |
| C32×C19×3−1+2 | 3 |
| C3×C9⋊H(3,𝔽3) | 19 |