Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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. #13068234 | C2 | semidirect |
| 3. #13066686 | C2 | semidirect |
| 4. #13066675 | C2 | semidirect |
| 39. C11×D8 | Q16 | semidirect |
| 125. D8 | Dic44 | semidirect |
| 139. C11 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070763 | 2 |
| #13068234 | 2 |
| #13066686 | 2 |
| #13066675 | 2 |
| C8×C11×D8 | 2 |
| #12447 | 11 |