Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 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. #13079355 | C2 | semidirect |
| 2. #13077521 | C2 | semidirect |
| 3. #13070832 | C2 | semidirect |
| 4. #13070784 | C2 | semidirect |
| 5. #13070693 | C2 | semidirect |
| 6. #13070692 | C2 | semidirect |
| 7. #13070563 | C2 | semidirect |
| 8. #13070513 | C2 | semidirect |
| 9. #13070511 | C2 | semidirect |
| 10. #13070427 | C2 | semidirect |
| 11. C11×#2230 | C2 | semidirect |
| 15. C11×#498 | C22 | semidirect |
| 25. #10622482 | C22 | semidirect |
| 31. #10622308 | C22 | semidirect |
| 33. C11×#365 | C22 | semidirect |
| 34. C11×#364 | C22 | semidirect |
| 36. #10622154 | C22 | semidirect |
| 38. #10622150 | C22 | semidirect |
| 39. #10622133 | C22 | semidirect |
| 41. #10622125 | C22 | semidirect |
| 42. #10622101 | C22 | semidirect |
| 114. C11×Q16 | #41 | semidirect |
| 116. C11×D8 | #41 | semidirect |
| 138. Dic44 | #41 | semidirect |
| 143. D88 | #41 | semidirect |
| 161. #2230 | D11 | semidirect |
| 214. #498 | C2×D11 | semidirect |
| 231. #365 | C2×D11 | semidirect |
| 233. #364 | C2×D11 | semidirect |
| 335. Q16 | #4343 | semidirect |
| 346. D8 | #4343 | semidirect |
| 376. C11 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079355 | 2 |
| #13077521 | 2 |
| #13070832 | 2 |
| #13070784 | 2 |
| #13070693 | 2 |
| #13070692 | 2 |
| #13070563 | 2 |
| #13070513 | 2 |
| #13070511 | 2 |
| #13070427 | 2 |
| C11×#2230 | 2 |
| #33688 | 11 |