Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. #13079129 | C2 | semidirect |
| 3. #13070861 | C2 | semidirect |
| 4. #13070859 | C2 | semidirect |
| 5. #13070858 | C2 | semidirect |
| 6. #13070854 | C2 | semidirect |
| 7. #13070322 | C2 | semidirect |
| 8. D11×#346 | C2 | semidirect |
| 9. C11×#2245 | C2 | semidirect |
| 111. #2245 | D11 | semidirect |
| 255. C11 | #33701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079129 | 2 |
| #13079045 | 2 |
| #13070861 | 2 |
| #13070859 | 2 |
| #13070858 | 2 |
| #13070854 | 2 |
| #13070322 | 2 |
| D11×#346 | 2 |
| C11×#2245 | 2 |
| #33701 | 11 |