Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
594 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 131 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. #13079276 | C2 | semidirect |
| 3. #13070887 | C2 | semidirect |
| 4. #13070871 | C2 | semidirect |
| 5. #13070850 | C2 | semidirect |
| 6. #13070677 | C2 | semidirect |
| 7. #13070655 | C2 | semidirect |
| 8. #13070557 | C2 | semidirect |
| 9. #13070546 | C2 | semidirect |
| 10. #13070424 | C2 | semidirect |
| 11. C11×#2244 | C2 | semidirect |
| 17. C11×#499 | C22 | semidirect |
| 23. C2×#66891 | C22 | semidirect |
| 26. C2×Dic88 | C22 | semidirect |
| 29. #10622486 | C22 | semidirect |
| 32. #10622312 | C22 | semidirect |
| 36. C11×#357 | C22 | semidirect |
| 37. C11×#346 | C22 | semidirect |
| 39. Dic11⋊C16 | C22 | semidirect |
| 40. #10622130 | C22 | semidirect |
| 42. C4×C11⋊C16 | C22 | semidirect |
| 144. #2244 | D11 | semidirect |
| 194. #499 | C2×D11 | semidirect |
| 212. #357 | C2×D11 | semidirect |
| 214. #346 | C2×D11 | semidirect |
| 336. C11 | #33788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079276 | 2 |
| #13079096 | 2 |
| #13070887 | 2 |
| #13070871 | 2 |
| #13070850 | 2 |
| #13070677 | 2 |
| #13070655 | 2 |
| #13070557 | 2 |
| #13070546 | 2 |
| #13070424 | 2 |
| C11×#2244 | 2 |
| #33788 | 11 |