Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
558 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 107 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. #13077333 | C2 | semidirect |
| 3. #13069439 | C2 | semidirect |
| 4. #13067285 | C2 | semidirect |
| 5. #13067175 | C2 | semidirect |
| 6. #13066446 | C2 | semidirect |
| 7. C11×#1286 | C2 | semidirect |
| 23. #10622308 | C4 | semidirect |
| 24. #10622307 | C4 | semidirect |
| 116. C2×C11⋊C8 | D8 | semidirect |
| 125. #1286 | 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 |
|---|---|
| #13079536 | 2 |
| #13077333 | 2 |
| #13069439 | 2 |
| #13067285 | 2 |
| #13067175 | 2 |
| #13066446 | 2 |
| C11×#1286 | 2 |
| #9293 | 11 |