Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3550 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 627 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. #13076868 | C2 | direct (N × H) |
| 2. C2×#10622286 | C2 | semidirect |
| 3. C2×#10622560 | C2 | semidirect |
| 4. C2×#10622844 | C2 | semidirect |
| 6. C2×C11×#393 | C2 | semidirect |
| 8. C23×Q8×C11 | C22 | semidirect |
| 9. C23×Dic22 | C22 | semidirect |
| 14. C11×#393 | C22 | semidirect |
| 15. C2×C11×#95 | C22 | semidirect |
| 16. #10622844 | C22 | semidirect |
| 17. C2×C11⋊#95 | C22 | semidirect |
| 18. C2×C11⋊#95 | C22 | semidirect |
| 20. #10622560 | C22 | semidirect |
| 21. #10622286 | C22 | semidirect |
| 25. C24×D11 | Q8 | semidirect |
| 29. C22×Q8×C11 | C23 | semidirect |
| 35. C22×Dic22 | C23 | semidirect |
| 44. C11×#95 | C23 | semidirect |
| 45. C11⋊#95 | C23 | semidirect |
| 46. C11⋊#95 | C23 | semidirect |
| 61. C23×D11 | C2×Q8 | semidirect |
| 86. C2×#393 | D11 | semidirect |
| 122. C23×Q8 | C2×D11 | semidirect |
| 130. #393 | C2×D11 | semidirect |
| 134. C2×#95 | C2×D11 | semidirect |
| 163. C22×Q8 | C22×D11 | semidirect |
| 177. #95 | C22×D11 | semidirect |
| 179. C2×C11 | #2840 | semidirect |
| 218. C11 | C2×#2840 | semidirect |
| 271. C2 | #13076868 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13076868 | 2 |
| C2×#10622286 | 2 |
| C2×#10622560 | 2 |
| C2×#10622844 | 2 |
| C2×#10622568 | 2 |
| C2×C11×#393 | 2 |
| C2×#2840 | 11 |