Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
538 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 147 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. D11×#500 | C2 | semidirect |
| 3. #13070891 | C2 | semidirect |
| 4. #13070889 | C2 | semidirect |
| 5. #13070839 | C2 | semidirect |
| 6. #13070795 | C2 | semidirect |
| 7. #13070751 | C2 | semidirect |
| 8. #13070413 | C2 | semidirect |
| 9. C11×#2240 | C2 | semidirect |
| 117. #2240 | D11 | semidirect |
| 274. C11 | #33792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079193 | 2 |
| D11×#500 | 2 |
| #13070891 | 2 |
| #13070889 | 2 |
| #13070839 | 2 |
| #13070795 | 2 |
| #13070751 | 2 |
| #13070413 | 2 |
| C11×#2240 | 2 |
| #33792 | 11 |