Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
526 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 121 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. #13079346 | C2 | semidirect |
| 2. #13077525 | C2 | semidirect |
| 3. #13070830 | C2 | semidirect |
| 4. #13070791 | C2 | semidirect |
| 5. #13070688 | C2 | semidirect |
| 6. #13070566 | C2 | semidirect |
| 8. #13070513 | C2 | semidirect |
| 9. #13070510 | C2 | semidirect |
| 10. #13070425 | C2 | semidirect |
| 11. C11×#2239 | C2 | semidirect |
| 17. #10622804 | C22 | semidirect |
| 18. #10622797 | C22 | semidirect |
| 29. #10622482 | C22 | semidirect |
| 30. #10622471 | C22 | semidirect |
| 33. C11×#365 | C22 | semidirect |
| 34. C11×#362 | C22 | semidirect |
| 38. #10622150 | C22 | semidirect |
| 39. #10622149 | C22 | semidirect |
| 40. #10622133 | C22 | semidirect |
| 41. #10622132 | C22 | semidirect |
| 146. #2239 | D11 | semidirect |
| 210. #365 | C2×D11 | semidirect |
| 212. #362 | C2×D11 | semidirect |
| 341. C11 | #33690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079346 | 2 |
| #13077525 | 2 |
| #13070830 | 2 |
| #13070791 | 2 |
| #13070688 | 2 |
| #13070566 | 2 |
| #13070564 | 2 |
| #13070513 | 2 |
| #13070510 | 2 |
| #13070425 | 2 |
| C11×#2239 | 2 |
| #33690 | 11 |