Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
558 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 113 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. #13077334 | C2 | semidirect |
| 3. #13069439 | C2 | semidirect |
| 4. #13067283 | C2 | semidirect |
| 5. #13066474 | C2 | semidirect |
| 6. #13066446 | C2 | semidirect |
| 7. C11×#1517 | C2 | semidirect |
| 14. #10622701 | C4 | semidirect |
| 15. #10622686 | C4 | semidirect |
| 119. C2×C11⋊C8 | D8 | semidirect |
| 124. #1517 | D11 | semidirect |
| 314. C11 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079531 | 2 |
| #13077334 | 2 |
| #13069439 | 2 |
| #13067283 | 2 |
| #13066474 | 2 |
| #13066446 | 2 |
| C11×#1517 | 2 |
| #9293 | 11 |