Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
578 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#10622691 | C2 | semidirect |
| 4. #13067289 | C2 | semidirect |
| 6. #13066454 | C2 | semidirect |
| 7. C11×#1966 | C2 | semidirect |
| 123. #1966 | D11 | semidirect |
| 294. C11 | #10174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079737 | 2 |
| C2×#10622691 | 2 |
| #13079075 | 2 |
| #13067289 | 2 |
| #13067066 | 2 |
| #13066454 | 2 |
| C11×#1966 | 2 |
| #10174 | 11 |