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. #13079203 | C2 | semidirect |
| 3. #13070872 | C2 | semidirect |
| 4. #13070871 | C2 | semidirect |
| 5. #13070841 | C2 | semidirect |
| 6. #13070655 | C2 | semidirect |
| 7. #13070546 | C2 | semidirect |
| 8. #13070413 | C2 | semidirect |
| 9. C11×#2240 | C2 | semidirect |
| 14. C11×#500 | C22 | semidirect |
| 18. C2×#66891 | C22 | semidirect |
| 21. C2×#66864 | C22 | semidirect |
| 25. #10622486 | C22 | semidirect |
| 26. #10622312 | 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 |
| 129. #2240 | D11 | semidirect |
| 162. C4×D11 | SD32 | semidirect |
| 175. #500 | C2×D11 | semidirect |
| 190. #357 | 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 |
|---|---|
| #13079203 | 2 |
| D11×#493 | 2 |
| #13070872 | 2 |
| #13070871 | 2 |
| #13070841 | 2 |
| #13070655 | 2 |
| #13070546 | 2 |
| #13070413 | 2 |
| C11×#2240 | 2 |
| #33774 | 11 |