Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1328 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 313 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. C3×3−1+2×C19⋊C3 | C3 | semidirect |
| 3. C32×C9×C19⋊C3 | C3 | semidirect |
| 4. #17987428 | C3 | semidirect |
| 5. #17987427 | C3 | semidirect |
| 6. #17987426 | C3 | semidirect |
| 7. #17987425 | C3 | semidirect |
| 8. #17987424 | C3 | semidirect |
| 9. #17987423 | C3 | semidirect |
| 10. #17987422 | C3 | semidirect |
| 11. C19⋊C3×C32⋊C9 | C3 | semidirect |
| 12. C19⋊C3×C32⋊C9 | C3 | semidirect |
| 13. C19×C9⋊H(3,𝔽3) | C3 | semidirect |
| 16. C3×#10587025 | C32 | semidirect |
| 17. C3×#10587022 | C32 | semidirect |
| 18. C3×#10587022 | C32 | semidirect |
| 19. C3×#10587023 | C32 | semidirect |
| 20. C3×#10587023 | C32 | semidirect |
| 26. C32×#4294 | C32 | semidirect |
| 31. C3×C9×C19⋊C3 | C32 | semidirect |
| 32. C3×C9×C19⋊C3 | C32 | semidirect |
| 33. C32⋊#4294 | C32 | semidirect |
| 34. C32⋊#4294 | C32 | semidirect |
| 35. C32⋊#4294 | C32 | semidirect |
| 36. #13095303 | C32 | semidirect |
| 37. #13095303 | C32 | semidirect |
| 38. #13095303 | C32 | semidirect |
| 39. #13095303 | C32 | semidirect |
| 40. #13095303 | C32 | semidirect |
| 41. C3×C19×3−1+2 | C32 | semidirect |
| 43. C32×C9×C19 | C32 | semidirect |
| 44. C19×C32⋊C9 | C32 | semidirect |
| 45. C19×C32⋊C9 | C32 | semidirect |
| 54. C32×C19⋊C3 | 3−1+2 | semidirect |
| 82. C9×C19⋊C3 | H(3,𝔽3) | semidirect |
| 93. C9⋊H(3,𝔽3) | C19⋊C3 | direct (N × H) |
| 101. C32×C19 | C3×3−1+2 | semidirect |
| 115. C3×C19⋊C3 | C3×3−1+2 | semidirect |
| 119. C9×C19 | C3×H(3,𝔽3) | semidirect |
| 123. #4294 | C3×H(3,𝔽3) | semidirect |
| 132. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 145. C32×C9 | C3×C19⋊C3 | semidirect |
| 154. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 155. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 164. C19⋊C3 | C9⋊H(3,𝔽3) | direct (N × H) |
| 201. C19 | C3×C9⋊H(3,𝔽3) | semidirect |
| 221. C32 | 3−1+2×C19⋊C3 | semidirect |
| 229. C9 | H(3,𝔽3)×C19⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C19⋊C3 | 3 |
| C3×H(3,𝔽3)×C19⋊C3 | 3 |
| C32×C9×C19⋊C3 | 3 |
| #17987428 | 3 |
| #17987427 | 3 |
| #17987426 | 3 |
| #17987425 | 3 |
| #17987424 | 3 |
| #17987423 | 3 |
| #17987422 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| C19×C9⋊H(3,𝔽3) | 3 |
| C3×C9⋊H(3,𝔽3) | 19 |