Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
240 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 83 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. #13067501 | C2 | semidirect |
| 2. D8×C11⋊C8 | C2 | semidirect |
| 3. #13066690 | C2 | semidirect |
| 4. #13066577 | C2 | semidirect |
| 5. #13066577 | C2 | semidirect |
| 6. #13066535 | C2 | semidirect |
| 52. C11×D8 | M16 | semidirect |
| 162. D8 | #4318 | semidirect |
| 180. C11 | #12073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13067501 | 2 |
| D8×C11⋊C8 | 2 |
| #13066690 | 2 |
| #13066577 | 2 |
| #13066535 | 2 |
| C4×C11×D16 | 2 |
| #12073 | 11 |