Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #13077694 | C2 | semidirect |
| 3. #13067125 | C2 | semidirect |
| 4. #13067125 | C2 | semidirect |
| 5. #13067084 | C2 | semidirect |
| 6. #13066444 | C2 | semidirect |
| 7. C11×#1287 | C2 | semidirect |
| 21. #10622308 | C4 | semidirect |
| 22. #10622307 | C4 | semidirect |
| 23. #10622306 | C4 | semidirect |
| 24. #10622294 | C4 | semidirect |
| 119. #1287 | D11 | semidirect |
| 291. C11 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079551 | 2 |
| #13077694 | 2 |
| #13067125 | 2 |
| #13067084 | 2 |
| #13066444 | 2 |
| C11×#1287 | 2 |
| #9281 | 11 |