Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
220 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 96 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. #17987573 | C3 | semidirect |
| 3. #17987572 | C3 | semidirect |
| 4. #17987571 | C3 | semidirect |
| 5. #17987570 | C3 | semidirect |
| 7. C9×#10587020 | C3 | semidirect |
| 8. C9×#10587020 | C3 | semidirect |
| 36. #10587022 | C27 | semidirect |
| 44. #10587020 | 3−1+2 | semidirect |
| 60. C9×C19 | C3×C27 | semidirect |
| 64. #4294 | C3×C27 | semidirect |
| 105. C19 | C27×3−1+2 | semidirect |
| 118. C9 | (C19⋊C3)⋊C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×(C19⋊C3)⋊C27 | 3 |
| #17987573 | 3 |
| #17987572 | 3 |
| #17987571 | 3 |
| #17987570 | 3 |
| #17987557 | 3 |
| C9×#10587020 | 3 |
| #17987410 | 3 |
| C27×3−1+2 | 19 |