Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
520 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 123 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. #13079362 | C2 | semidirect |
| 3. #13070837 | C2 | semidirect |
| 4. #13070784 | C2 | semidirect |
| 5. #13070698 | C2 | semidirect |
| 6. #13070697 | C2 | semidirect |
| 8. #13070506 | C2 | semidirect |
| 9. #13070504 | C2 | semidirect |
| 10. #13070427 | C2 | semidirect |
| 11. C11×#2230 | C2 | semidirect |
| 15. C11×#498 | C22 | semidirect |
| 27. #10622466 | C22 | semidirect |
| 31. #10622312 | C22 | semidirect |
| 33. C11×#365 | C22 | semidirect |
| 34. C11×#364 | C22 | semidirect |
| 36. #10622155 | C22 | semidirect |
| 38. #10622150 | C22 | semidirect |
| 39. #10622134 | C22 | semidirect |
| 41. #10622125 | C22 | semidirect |
| 42. #10622101 | C22 | semidirect |
| 160. #2230 | D11 | semidirect |
| 209. #498 | C2×D11 | semidirect |
| 226. #365 | C2×D11 | semidirect |
| 228. #364 | C2×D11 | semidirect |
| 367. C11 | #33689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079362 | 2 |
| #13077521 | 2 |
| #13070837 | 2 |
| #13070784 | 2 |
| #13070698 | 2 |
| #13070697 | 2 |
| #13070568 | 2 |
| #13070506 | 2 |
| #13070504 | 2 |
| #13070427 | 2 |
| C11×#2230 | 2 |
| #33689 | 11 |