Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #13068609 | C2 | semidirect |
| 5. C2×#10622094 | C2 | semidirect |
| 6. #13066490 | C2 | semidirect |
| 7. C11×#1566 | C2 | semidirect |
| 123. #1566 | D11 | semidirect |
| 308. C11 | #10459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13078090 | 2 |
| #13068609 | 2 |
| #13067294 | 2 |
| #13067068 | 2 |
| C2×#10622094 | 2 |
| #13066490 | 2 |
| C11×#1566 | 2 |
| #10459 | 11 |