Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 131 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. #13077520 | C2 | semidirect |
| 2. #13070828 | C2 | semidirect |
| 3. #13070789 | C2 | semidirect |
| 4. #13070689 | C2 | semidirect |
| 5. #13070561 | C2 | semidirect |
| 6. #13070512 | C2 | semidirect |
| 7. #13070432 | C2 | semidirect |
| 8. C11×#3176 | C2 | semidirect |
| 12. C11×#499 | C22 | semidirect |
| 13. C11×#493 | C22 | semidirect |
| 17. C11×#442 | C22 | semidirect |
| 27. #10622201 | C22 | semidirect |
| 30. #10622125 | C22 | semidirect |
| 31. #10622104 | C22 | semidirect |
| 32. #10622101 | C22 | semidirect |
| 117. #3176 | D11 | semidirect |
| 159. #499 | C2×D11 | semidirect |
| 160. #493 | C2×D11 | semidirect |
| 168. #442 | C2×D11 | semidirect |
| 282. C11 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077520 | 2 |
| #13070828 | 2 |
| #13070789 | 2 |
| #13070689 | 2 |
| #13070561 | 2 |
| #13070512 | 2 |
| #13070432 | 2 |
| C11×#3176 | 2 |
| #33692 | 11 |