Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
576 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 127 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. #13078287 | C2 | semidirect |
| 2. #13070817 | C2 | semidirect |
| 3. #13070798 | C2 | semidirect |
| 4. #13070731 | C2 | semidirect |
| 5. #13070702 | C2 | semidirect |
| 6. #13070555 | C2 | semidirect |
| 7. #13070542 | C2 | semidirect |
| 8. #13070229 | C2 | semidirect |
| 9. C11×#2216 | C2 | semidirect |
| 119. #2216 | D11 | semidirect |
| 280. C11 | #33769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13078287 | 2 |
| #13070817 | 2 |
| #13070798 | 2 |
| #13070731 | 2 |
| #13070702 | 2 |
| #13070555 | 2 |
| #13070542 | 2 |
| #13070229 | 2 |
| C11×#2216 | 2 |
| #33769 | 11 |