Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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. #13067333 | C2 | semidirect |
| 5. #13067128 | C2 | semidirect |
| 6. #13066510 | C2 | semidirect |
| 7. C11×#3165 | C2 | semidirect |
| 123. #3165 | D11 | semidirect |
| 300. C11 | #10100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079615 | 2 |
| #13074557 | 2 |
| #13067333 | 2 |
| #13067213 | 2 |
| #13067128 | 2 |
| #13066510 | 2 |
| C11×#3165 | 2 |
| #10100 | 11 |