Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
730 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 147 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. #13079196 | C2 | semidirect |
| 2. D11×#493 | C2 | semidirect |
| 3. #13070866 | C2 | semidirect |
| 4. #13070865 | C2 | semidirect |
| 5. #13070841 | C2 | semidirect |
| 6. #13070650 | C2 | semidirect |
| 7. #13070529 | C2 | semidirect |
| 8. #13070413 | C2 | semidirect |
| 9. C11×#2240 | C2 | semidirect |
| 14. C11×#500 | C22 | semidirect |
| 18. C2×#66890 | C22 | semidirect |
| 21. C2×D176 | C22 | semidirect |
| 25. #10622485 | C22 | semidirect |
| 27. #10622308 | C22 | semidirect |
| 29. C11×#357 | C22 | semidirect |
| 30. C4×C11×C16 | C22 | semidirect |
| 32. Dic11⋊C16 | C22 | semidirect |
| 33. #10622129 | C22 | semidirect |
| 34. C4×C11⋊C16 | C22 | semidirect |
| 130. #2240 | D11 | semidirect |
| 169. C4×D11 | D16 | semidirect |
| 180. #500 | C2×D11 | semidirect |
| 195. #357 | C2×D11 | semidirect |
| 198. C4×C16 | C2×D11 | semidirect |
| 317. C11 | #33771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079196 | 2 |
| D11×#493 | 2 |
| #13070866 | 2 |
| #13070865 | 2 |
| #13070841 | 2 |
| #13070650 | 2 |
| #13070529 | 2 |
| #13070413 | 2 |
| C11×#2240 | 2 |
| #33771 | 11 |