Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
638 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 135 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. #13081641 | C2 | semidirect |
| 2. #13080554 | C2 | semidirect |
| 3. #13068085 | C2 | semidirect |
| 4. #13068050 | C2 | semidirect |
| 5. #13067869 | C2 | semidirect |
| 6. #13067678 | C2 | semidirect |
| 7. #13067514 | C2 | semidirect |
| 8. C8×D88 | C2 | semidirect |
| 9. C11×#1706 | C2 | semidirect |
| 126. #1706 | D11 | semidirect |
| 299. C11 | #19961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081641 | 2 |
| #13080554 | 2 |
| #13068085 | 2 |
| #13068050 | 2 |
| #13067869 | 2 |
| #13067678 | 2 |
| #13067514 | 2 |
| C8×D88 | 2 |
| C11×#1706 | 2 |
| #19961 | 11 |