Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
586 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 131 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. #13079267 | C2 | semidirect |
| 2. #13079104 | C2 | semidirect |
| 3. #13070882 | C2 | semidirect |
| 4. #13070873 | C2 | semidirect |
| 5. #13070850 | C2 | semidirect |
| 6. #13070674 | C2 | semidirect |
| 7. #13070660 | C2 | semidirect |
| 8. #13070542 | C2 | semidirect |
| 9. #13070534 | C2 | semidirect |
| 10. #13070424 | C2 | semidirect |
| 11. C11×#2245 | C2 | semidirect |
| 144. #2245 | D11 | semidirect |
| 334. C11 | #33787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079267 | 2 |
| #13079104 | 2 |
| #13070882 | 2 |
| #13070873 | 2 |
| #13070850 | 2 |
| #13070674 | 2 |
| #13070660 | 2 |
| #13070542 | 2 |
| #13070534 | 2 |
| #13070424 | 2 |
| C11×#2245 | 2 |
| #33787 | 11 |