Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
192 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 78 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. #17987555 | C3 | semidirect |
| 8. C9×#10587020 | C3 | semidirect |
| 44. #10587020 | 3−1+2 | semidirect |
| 59. C9×C19 | C27⋊C3 | semidirect |
| 105. C19 | #10624728 | semidirect |
| 118. C9 | #13095342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095342 | 3 |
| #17987573 | 3 |
| #17987572 | 3 |
| #17987571 | 3 |
| #17987570 | 3 |
| C32⋊#10587020 | 3 |
| #17987555 | 3 |
| C9×#10587020 | 3 |
| 3−1+2×#4294 | 3 |
| #10624728 | 19 |