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. #13078281 | C2 | semidirect |
| 2. #13070820 | C2 | semidirect |
| 3. #13070795 | C2 | semidirect |
| 4. #13070727 | C2 | semidirect |
| 5. #13070707 | C2 | semidirect |
| 6. #13070557 | C2 | semidirect |
| 7. #13070536 | C2 | semidirect |
| 8. #13070229 | C2 | semidirect |
| 9. C11×#2215 | C2 | semidirect |
| 120. #2215 | 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 |
|---|---|
| #13078281 | 2 |
| #13070820 | 2 |
| #13070795 | 2 |
| #13070727 | 2 |
| #13070707 | 2 |
| #13070557 | 2 |
| #13070536 | 2 |
| #13070229 | 2 |
| C11×#2215 | 2 |
| #33769 | 11 |