Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
686 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 686 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. #13079200 | C2 | semidirect |
| 3. #13070873 | C2 | semidirect |
| 4. #13070840 | C2 | semidirect |
| 5. #13070839 | C2 | semidirect |
| 6. #13070654 | C2 | semidirect |
| 7. #13070543 | C2 | semidirect |
| 8. #13070413 | C2 | semidirect |
| 9. C11×#2248 | C2 | semidirect |
| 14. C2×C11×SD32 | C22 | semidirect |
| 15. C11×#494 | C22 | semidirect |
| 20. Q16×Dic11 | C22 | semidirect |
| 21. C2×#66892 | C22 | semidirect |
| 28. #10622295 | C22 | semidirect |
| 29. C4×C11×C16 | C22 | semidirect |
| 30. #10622200 | C22 | semidirect |
| 31. #10622147 | C22 | semidirect |
| 33. Dic11⋊C16 | C22 | semidirect |
| 34. C4×C11⋊C16 | C22 | semidirect |
| 127. #2248 | D11 | semidirect |
| 163. C4×D11 | SD32 | semidirect |
| 174. C2×SD32 | C2×D11 | semidirect |
| 176. #494 | C2×D11 | semidirect |
| 193. C4×C16 | C2×D11 | semidirect |
| 308. C11 | #33774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079200 | 2 |
| D11×#493 | 2 |
| #13070873 | 2 |
| #13070840 | 2 |
| #13070839 | 2 |
| #13070654 | 2 |
| #13070543 | 2 |
| #13070413 | 2 |
| C11×#2248 | 2 |
| #33774 | 11 |