Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #10623050 | C2 | semidirect |
| 3. C11×#405 | C2 | semidirect |
| 4. #10622746 | C2 | semidirect |
| 5. #10622744 | C2 | semidirect |
| 6. #10622726 | C2 | semidirect |
| 7. C2×#66885 | C2 | semidirect |
| 8. #10622327 | C2 | semidirect |
| 9. #10622326 | C2 | semidirect |
| 10. #10622310 | C2 | semidirect |
| 11. #10622307 | C2 | semidirect |
| 27. #66923 | C22 | semidirect |
| 28. #66922 | C22 | semidirect |
| 29. C11×#97 | C22 | semidirect |
| 30. C4×C8×C11 | C22 | semidirect |
| 35. #66885 | C22 | semidirect |
| 36. #66885 | C22 | semidirect |
| 37. #66885 | C22 | semidirect |
| 38. #66880 | C22 | semidirect |
| 39. #66880 | C22 | semidirect |
| 40. #66880 | C22 | semidirect |
| 120. #405 | D11 | semidirect |
| 168. #97 | C2×D11 | semidirect |
| 169. C4×C8 | C2×D11 | semidirect |
| 212. C11 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623056 | 2 |
| #10623050 | 2 |
| C11×#405 | 2 |
| #10622746 | 2 |
| #10622744 | 2 |
| #10622726 | 2 |
| C2×#66885 | 2 |
| #10622327 | 2 |
| #10622326 | 2 |
| #10622310 | 2 |
| #10622307 | 2 |
| #3136 | 11 |