Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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. #10623086 | C2 | semidirect |
| 2. D4×D44 | C2 | semidirect |
| 3. C8×D4×C11 | C2 | semidirect |
| 4. #10622728 | C2 | semidirect |
| 5. C2×#66885 | C2 | semidirect |
| 6. #10622459 | C2 | semidirect |
| 7. #10622456 | C2 | semidirect |
| 8. #10622349 | C2 | semidirect |
| 9. #10622345 | C2 | semidirect |
| 10. #10622307 | C2 | semidirect |
| 11. C4×D88 | C2 | semidirect |
| 15. C22×C8×C11 | C22 | semidirect |
| 18. #66983 | C22 | semidirect |
| 19. C2×C4⋊Dic11 | C22 | semidirect |
| 21. C2×D88 | C22 | semidirect |
| 28. C4×D44 | C22 | semidirect |
| 29. #66922 | C22 | semidirect |
| 30. C11×C4⋊C8 | C22 | semidirect |
| 31. C11×C22⋊C8 | C22 | semidirect |
| 32. C4×C8×C11 | C22 | semidirect |
| 35. #66885 | C22 | semidirect |
| 36. #66885 | C22 | semidirect |
| 37. #66885 | C22 | semidirect |
| 38. #66885 | C22 | semidirect |
| 39. #66882 | C22 | semidirect |
| 40. #66882 | C22 | semidirect |
| 86. D4×C11 | D8 | semidirect |
| 107. D44 | #41 | semidirect |
| 123. C8×D4 | D11 | semidirect |
| 152. C22×C8 | C2×D11 | semidirect |
| 167. C4⋊C8 | C2×D11 | semidirect |
| 174. C22⋊C8 | C2×D11 | semidirect |
| 175. C4×C8 | C2×D11 | semidirect |
| 220. C11 | #3294 | semidirect |
| 240. D4 | D88 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623086 | 2 |
| D4×D44 | 2 |
| C8×D4×C11 | 2 |
| #10622728 | 2 |
| C2×#66885 | 2 |
| #10622459 | 2 |
| #10622456 | 2 |
| #10622349 | 2 |
| #10622345 | 2 |
| #10622307 | 2 |
| C4×D88 | 2 |
| #3294 | 11 |