Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
600 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 600 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 |
|---|---|---|
| 1. #13079554 | C2 | semidirect |
| 3. #13067329 | C2 | semidirect |
| 4. #13067231 | C2 | semidirect |
| 5. #13066968 | C2 | semidirect |
| 6. #13066514 | C2 | semidirect |
| 7. C11×#3215 | C2 | semidirect |
| 128. #3215 | D11 | semidirect |
| 320. C11 | #10129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079554 | 2 |
| C2×#10622671 | 2 |
| #13067329 | 2 |
| #13067231 | 2 |
| #13066968 | 2 |
| #13066514 | 2 |
| C11×#3215 | 2 |
| #10129 | 11 |