Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
212 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #17987578 | C3 | semidirect |
| 4. #17987576 | C3 | semidirect |
| 5. #17987574 | C3 | semidirect |
| 17. #13095312 | C9 | semidirect |
| 19. #13095310 | C9 | semidirect |
| 20. C27×C19⋊C3 | C9 | semidirect |
| 21. C19×C27⋊C3 | C9 | semidirect |
| 37. C19×C27 | C3×C9 | semidirect |
| 38. #10587018 | C3×C9 | semidirect |
| 66. C27⋊C3 | #4296 | semidirect |
| 77. C19⋊C3 | #6875 | semidirect |
| 93. C27 | C3×#4296 | semidirect |
| 94. C19 | C3×#6875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C19⋊C3)⋊(C27⋊C3) | 3 |
| C3×#13095338 | 3 |
| #17987578 | 3 |
| #17987576 | 3 |
| #17987574 | 3 |
| C19⋊C3×C27⋊C3 | 3 |
| C3×#6875 | 19 |