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×#13095332 | C3 | direct (N × H) |
| 2. C32×#10587025 | C3 | semidirect |
| 3. C32×#10587022 | C3 | semidirect |
| 4. C32×#10587023 | C3 | semidirect |
| 6. C32×C9×C19⋊C3 | C3 | semidirect |
| 7. C33×C9×C19 | C3 | semidirect |
| 9. #13095332 | C32 | direct (N × H) |
| 10. C3×#10587025 | C32 | semidirect |
| 11. C3×#10587022 | C32 | semidirect |
| 12. C3×#10587023 | C32 | semidirect |
| 15. C3×C9×C19⋊C3 | C32 | semidirect |
| 20. C32×C9×C19 | C32 | semidirect |
| 30. C3×C9×C19 | C33 | semidirect |
| 32. #10587025 | C33 | semidirect |
| 34. #10587023 | C33 | semidirect |
| 35. #10587022 | C33 | semidirect |
| 36. C9×C19⋊C3 | C33 | semidirect |
| 43. C33×C9 | C19⋊C3 | semidirect |
| 45. C32×C19 | #737 | semidirect |
| 66. C32×C9 | C3×C19⋊C3 | semidirect |
| 68. C3×C19 | C3×#737 | semidirect |
| 85. C3×C9 | C32×C19⋊C3 | semidirect |
| 86. C19 | C32×#737 | semidirect |
| 90. C32 | #13095332 | direct (N × H) |
| 99. C3 | C3×#13095332 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095332 | 3 |
| C32×#10587025 | 3 |
| C32×#10587022 | 3 |
| C32×#10587023 | 3 |
| C32×C32⋊(C19⋊C3) | 3 |
| C32×C9×C19⋊C3 | 3 |
| C33×C9×C19 | 3 |
| C32×#737 | 19 |