Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
442 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 85 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. #13077686 | C2 | semidirect |
| 3. #13067250 | C2 | semidirect |
| 4. #13067164 | C2 | semidirect |
| 5. #13067164 | C2 | semidirect |
| 6. #13066481 | C2 | semidirect |
| 7. C11×#1291 | C2 | semidirect |
| 20. #10622308 | C4 | semidirect |
| 21. #10622307 | C4 | semidirect |
| 22. #10622307 | C4 | semidirect |
| 23. #10622293 | C4 | semidirect |
| 113. #1291 | D11 | semidirect |
| 274. C11 | #9417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079354 | 2 |
| #13077686 | 2 |
| #13067250 | 2 |
| #13067164 | 2 |
| #13066481 | 2 |
| C11×#1291 | 2 |
| #9417 | 11 |