Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 159 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. D11×#499 | C2 | semidirect |
| 3. #13070859 | C2 | semidirect |
| 4. #13070858 | C2 | semidirect |
| 5. #13070857 | C2 | semidirect |
| 6. #13070856 | C2 | semidirect |
| 7. D11×#357 | C2 | semidirect |
| 8. D11×#346 | C2 | semidirect |
| 9. C11×#2244 | C2 | semidirect |
| 14. C11×#499 | C22 | semidirect |
| 22. #10622491 | C22 | semidirect |
| 27. #10622296 | C22 | semidirect |
| 28. C11×#357 | C22 | semidirect |
| 29. C11×#346 | C22 | semidirect |
| 30. #10622200 | C22 | semidirect |
| 31. #10622147 | C22 | semidirect |
| 32. #10622140 | C22 | semidirect |
| 33. #10622129 | C22 | semidirect |
| 34. #10622099 | C22 | semidirect |
| 115. #2244 | D11 | direct (N × H) |
| 154. #499 | C2×D11 | semidirect |
| 166. #357 | C2×D11 | semidirect |
| 169. #346 | C2×D11 | semidirect |
| 225. D11 | #2244 | direct (N × H) |
| 263. C11 | C2×#2244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D11×#499 | 2 |
| D11×#493 | 2 |
| #13070859 | 2 |
| #13070858 | 2 |
| #13070857 | 2 |
| #13070856 | 2 |
| D11×#357 | 2 |
| D11×#346 | 2 |
| C11×#2244 | 2 |
| C2×#2244 | 11 |