Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
758 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 107 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. #13079531 | C2 | semidirect |
| 2. #13079069 | C2 | semidirect |
| 3. C2×#10622308 | C2 | semidirect |
| 4. #13069455 | C2 | semidirect |
| 5. #13067285 | C2 | semidirect |
| 6. #13066453 | C2 | semidirect |
| 7. C11×#1492 | C2 | semidirect |
| 123. #4318 | D8 | semidirect |
| 132. #1492 | D11 | semidirect |
| 328. C11 | #10144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079531 | 2 |
| #13079069 | 2 |
| C2×#10622308 | 2 |
| #13069455 | 2 |
| #13067285 | 2 |
| #13066453 | 2 |
| C11×#1492 | 2 |
| #10144 | 11 |