Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
636 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 151 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. #13081769 | C2 | semidirect |
| 2. #13080421 | C2 | semidirect |
| 3. #13070869 | C2 | semidirect |
| 4. #13070741 | C2 | semidirect |
| 5. #13070698 | C2 | semidirect |
| 6. #13070596 | C2 | semidirect |
| 7. #13070498 | C2 | semidirect |
| 8. C11×#2170 | C2 | semidirect |
| 110. #2170 | D11 | semidirect |
| 240. C11 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081769 | 2 |
| #13080421 | 2 |
| #13070869 | 2 |
| #13070741 | 2 |
| #13070698 | 2 |
| #13070596 | 2 |
| #13070498 | 2 |
| C11×#2170 | 2 |
| #33860 | 11 |