Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 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. #13081017 | C2 | semidirect |
| 2. #13070810 | C2 | semidirect |
| 3. #13070798 | C2 | semidirect |
| 4. #13070770 | C2 | semidirect |
| 5. #13070720 | C2 | semidirect |
| 6. C4×D176 | C2 | semidirect |
| 7. #13070449 | C2 | semidirect |
| 8. #13070403 | C2 | semidirect |
| 9. C11×#2253 | C2 | semidirect |
| 98. #2253 | D11 | semidirect |
| 234. C11 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081017 | 2 |
| #13070810 | 2 |
| #13070798 | 2 |
| #13070770 | 2 |
| #13070720 | 2 |
| C4×D176 | 2 |
| #13070449 | 2 |
| #13070403 | 2 |
| C11×#2253 | 2 |
| #33922 | 11 |