Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
2636 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 2636 conjugacy classes of subgroups — too many to draw. Only its 355 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 |
|---|---|---|
| 2. C3×3−1+2×C19⋊C3 | C3 | semidirect |
| 3. #17987421 | C3 | semidirect |
| 4. #17987420 | C3 | semidirect |
| 5. #17987419 | C3 | semidirect |
| 6. #17987418 | C3 | semidirect |
| 7. C19⋊C3×C32⋊C9 | C3 | semidirect |
| 8. C19×#6891 | C3 | semidirect |
| 16. C3×#10587025 | C32 | semidirect |
| 17. C3×#10587022 | C32 | semidirect |
| 18. C3×#10587023 | C32 | semidirect |
| 20. C3×C9×C19⋊C3 | C32 | semidirect |
| 21. C32⋊#4294 | C32 | semidirect |
| 22. #13095303 | C32 | semidirect |
| 24. C3×C19×3−1+2 | C32 | semidirect |
| 25. C19×C32⋊C9 | C32 | semidirect |
| 44. C32×C19⋊C3 | 3−1+2 | semidirect |
| 50. C3×C9×C19 | C33 | semidirect |
| 52. C3×#4294 | C33 | semidirect |
| 62. #6891 | C19⋊C3 | direct (N × H) |
| 69. C32×C19 | C3×3−1+2 | semidirect |
| 85. C3×C19⋊C3 | C3×3−1+2 | semidirect |
| 100. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 104. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 112. C19⋊C3 | #6891 | direct (N × H) |
| 141. C3×C9 | C32×C19⋊C3 | semidirect |
| 142. C19 | C3×#6891 | semidirect |
| 163. C32 | 3−1+2×C19⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C19⋊C3 | 3 |
| C3×3−1+2×C19⋊C3 | 3 |
| #17987421 | 3 |
| #17987420 | 3 |
| #17987419 | 3 |
| #17987418 | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| C19×#6891 | 3 |
| C3×#6891 | 19 |