Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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×C11×#131 | C2 | semidirect |
| 2. #10623364 | C2 | semidirect |
| 3. #10623361 | C2 | semidirect |
| 4. C2×#66961 | C2 | semidirect |
| 5. #10622748 | C2 | semidirect |
| 6. #10622747 | C2 | semidirect |
| 7. #10622734 | C2 | semidirect |
| 8. #10622728 | C2 | semidirect |
| 9. #10622727 | C2 | semidirect |
| 10. #10622726 | C2 | semidirect |
| 11. C2×#66885 | C2 | semidirect |
| 17. C2×C11×M16 | C22 | semidirect |
| 19. C22×C8×C11 | C22 | semidirect |
| 28. #66983 | C22 | semidirect |
| 31. #66977 | C22 | semidirect |
| 37. #66885 | C22 | semidirect |
| 38. #66885 | C22 | semidirect |
| 39. #66882 | C22 | semidirect |
| 40. #66881 | C22 | semidirect |
| 41. #66880 | C22 | semidirect |
| 42. #66880 | C22 | semidirect |
| 66. C11×M16 | D4 | semidirect |
| 124. C2×#131 | D11 | semidirect |
| 164. C2×M16 | C2×D11 | semidirect |
| 166. C22×C8 | C2×D11 | semidirect |
| 219. M16 | C22⋊D11 | semidirect |
| 236. C11 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#131 | 2 |
| #10623364 | 2 |
| #10623361 | 2 |
| C2×#66961 | 2 |
| #10622748 | 2 |
| #10622747 | 2 |
| #10622734 | 2 |
| #10622728 | 2 |
| #10622727 | 2 |
| #10622726 | 2 |
| C2×#66885 | 2 |
| #3062 | 11 |