Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
222 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #13068226 | C2 | semidirect |
| 4. #13066686 | C2 | semidirect |
| 5. #13066675 | C2 | semidirect |
| 6. #13066672 | C2 | semidirect |
| 169. C11 | #12449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070763 | 2 |
| #13070753 | 2 |
| #13068226 | 2 |
| #13066686 | 2 |
| #13066675 | 2 |
| #13066672 | 2 |
| C8×C11×D8 | 2 |
| #12449 | 11 |