Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
600 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 83 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. #13079621 | C2 | semidirect |
| 2. #13079557 | C2 | semidirect |
| 4. #13067232 | C2 | semidirect |
| 5. #13066969 | C2 | semidirect |
| 6. #13066514 | C2 | semidirect |
| 7. C11×#1555 | C2 | semidirect |
| 131. #1555 | D11 | semidirect |
| 320. C11 | #10129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079621 | 2 |
| #13079557 | 2 |
| C2×#10622687 | 2 |
| #13067232 | 2 |
| #13066969 | 2 |
| #13066514 | 2 |
| C11×#1555 | 2 |
| #10129 | 11 |