Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
392 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 103 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. #13067379 | C2 | semidirect |
| 3. #13067217 | C2 | semidirect |
| 5. #13066971 | C2 | semidirect |
| 7. C8×C11×M16 | C2 | semidirect |
| 123. C8×M16 | D11 | semidirect |
| 290. C11 | #9789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622310 | 2 |
| #13067379 | 2 |
| #13067217 | 2 |
| #13067213 | 2 |
| #13066971 | 2 |
| #13066967 | 2 |
| C8×C11×M16 | 2 |
| #9789 | 11 |