Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
622 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 622 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. #13079605 | C2 | semidirect |
| 2. #13079534 | C2 | semidirect |
| 3. C2×#10622687 | C2 | semidirect |
| 4. #13067228 | C2 | semidirect |
| 5. #13066969 | C2 | semidirect |
| 6. #13066514 | C2 | semidirect |
| 7. C11×#1555 | C2 | semidirect |
| 132. #1555 | D11 | semidirect |
| 329. C11 | #10128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079605 | 2 |
| #13079534 | 2 |
| C2×#10622687 | 2 |
| #13067228 | 2 |
| #13066969 | 2 |
| #13066514 | 2 |
| C11×#1555 | 2 |
| #10128 | 11 |