Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
5804 conjugacy classes of subgroups; only the 2920 normal subgroups are shown.
This group has 5804 conjugacy classes of subgroups — too many to draw. Only its 2920 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 | direct (N × H) |
| 2. C32×#10587025 | C3 | semidirect |
| 3. C32×#10587022 | C3 | semidirect |
| 4. C32×#10587023 | C3 | semidirect |
| 6. C33×#4294 | C3 | semidirect |
| 7. C32×C9×C19⋊C3 | C3 | semidirect |
| 8. C32×C19×3−1+2 | C3 | semidirect |
| 10. #13095333 | C32 | direct (N × H) |
| 11. C3×#10587025 | C32 | semidirect |
| 12. C3×#10587022 | C32 | semidirect |
| 13. C3×#10587023 | C32 | semidirect |
| 19. C32×#4294 | C32 | semidirect |
| 20. C3×C9×C19⋊C3 | C32 | semidirect |
| 22. C3×C19×3−1+2 | C32 | semidirect |
| 30. C19×3−1+2 | C33 | semidirect |
| 33. #10587025 | C33 | semidirect |
| 38. C3×#4294 | C33 | semidirect |
| 39. #10587023 | C33 | semidirect |
| 40. #10587022 | C33 | semidirect |
| 41. C9×C19⋊C3 | C33 | semidirect |
| 46. C32×3−1+2 | C19⋊C3 | semidirect |
| 51. C32×C19 | #737 | semidirect |
| 67. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 77. C3×C19 | C3×#737 | semidirect |
| 88. 3−1+2 | C32×C19⋊C3 | semidirect |
| 97. C19 | C32×#737 | semidirect |
| 101. C32 | #13095333 | direct (N × H) |
| 111. C3 | C3×#13095333 | 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 |
| C32×#10587025 | 3 |
| C32×#10587022 | 3 |
| C32×#10587023 | 3 |
| C32×C32⋊(C19⋊C3) | 3 |
| C33×#4294 | 3 |
| C32×C9×C19⋊C3 | 3 |
| C32×C19×3−1+2 | 3 |
| C32×#737 | 19 |