Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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. C22×C11×D8 | C2 | semidirect |
| 2. #10623336 | C2 | semidirect |
| 3. C2×#66985 | C2 | semidirect |
| 4. C2×#66957 | C2 | semidirect |
| 5. #10622768 | C2 | semidirect |
| 6. #10622767 | C2 | semidirect |
| 7. #10622764 | C2 | semidirect |
| 8. #10622714 | C2 | semidirect |
| 16. #66993 | C22 | semidirect |
| 18. #66989 | C22 | semidirect |
| 19. C2×#4324 | C22 | semidirect |
| 21. C2×#4323 | C22 | semidirect |
| 24. C2×Dic44 | C22 | semidirect |
| 26. C2×D88 | C22 | semidirect |
| 27. C2×#4314 | C22 | semidirect |
| 28. #66879 | C22 | semidirect |
| 29. C8×Dic11 | C22 | semidirect |
| 45. C2×C8×C11 | D4 | semidirect |
| 54. #4318 | D4 | semidirect |
| 86. C22×D8 | D11 | semidirect |
| 153. C2×C8 | C22⋊D11 | semidirect |
| 160. C11 | #3155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×D8 | 2 |
| #10623336 | 2 |
| C2×#66985 | 2 |
| C2×#66957 | 2 |
| #10622768 | 2 |
| #10622767 | 2 |
| #10622764 | 2 |
| #10622714 | 2 |
| #3155 | 11 |