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. #13070888 | C2 | semidirect |
| 4. #13070872 | C2 | semidirect |
| 5. #13070859 | C2 | semidirect |
| 6. #13070681 | C2 | semidirect |
| 7. #13070655 | C2 | semidirect |
| 8. #13070559 | C2 | semidirect |
| 9. #13070546 | C2 | semidirect |
| 10. #13070421 | C2 | semidirect |
| 11. C11×#2242 | C2 | semidirect |
| 17. C11×#499 | C22 | semidirect |
| 20. C2×#66893 | C22 | semidirect |
| 27. C2×#66864 | C22 | semidirect |
| 29. #10622486 | C22 | semidirect |
| 32. #10622312 | C22 | semidirect |
| 35. C11×#358 | C22 | semidirect |
| 37. C4×C11×C16 | C22 | semidirect |
| 39. Dic11⋊C16 | C22 | semidirect |
| 41. #10622129 | C22 | semidirect |
| 42. #10622099 | C22 | semidirect |
| 145. #2242 | D11 | semidirect |
| 194. #499 | C2×D11 | semidirect |
| 209. #358 | C2×D11 | semidirect |
| 215. C4×C16 | 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 |
| #13079098 | 2 |
| #13070888 | 2 |
| #13070872 | 2 |
| #13070859 | 2 |
| #13070681 | 2 |
| #13070655 | 2 |
| #13070559 | 2 |
| #13070546 | 2 |
| #13070421 | 2 |
| C11×#2242 | 2 |
| #33788 | 11 |