Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 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. C2×#10622525 | C2 | semidirect |
| 2. C2×D11×D16 | C2 | semidirect |
| 3. #13070927 | C2 | direct (N × H) |
| 4. C2×#10622087 | C2 | semidirect |
| 5. C2×#10622158 | C2 | semidirect |
| 6. C2×#10622157 | C2 | semidirect |
| 7. C2×#10622085 | C2 | semidirect |
| 8. C2×C11×D32 | C2 | semidirect |
| 12. C2×C11×D16 | C22 | semidirect |
| 16. #10622525 | C22 | semidirect |
| 18. D11×D16 | C22 | semidirect |
| 19. C2×Dic88 | C22 | semidirect |
| 22. C11×D32 | C22 | semidirect |
| 23. C2×C11×C32 | C22 | semidirect |
| 24. #10622158 | C22 | semidirect |
| 25. #10622157 | C22 | semidirect |
| 26. C2×C11⋊C32 | C22 | semidirect |
| 27. #10622087 | C22 | semidirect |
| 28. #10622085 | C22 | semidirect |
| 45. C11×D16 | C23 | semidirect |
| 51. Dic88 | C23 | semidirect |
| 56. C11×C32 | C23 | semidirect |
| 57. C11⋊C32 | C23 | semidirect |
| 95. C2×D32 | D11 | semidirect |
| 133. C2×D16 | C2×D11 | semidirect |
| 138. D32 | C2×D11 | semidirect |
| 141. C2×C32 | C2×D11 | semidirect |
| 178. D16 | C22×D11 | semidirect |
| 184. C32 | C22×D11 | semidirect |
| 187. C2×C11 | #2263 | semidirect |
| 221. C11 | C2×#2263 | semidirect |
| 265. C2 | #13070927 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622525 | 2 |
| C2×D11×D16 | 2 |
| #13070927 | 2 |
| C2×#10622087 | 2 |
| C2×#10622158 | 2 |
| C2×#10622157 | 2 |
| C2×#10622085 | 2 |
| C2×C11×D32 | 2 |
| C2×#2263 | 11 |