Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 2. #10623074 | C2 | semidirect |
| 3. C8×D4×C11 | C2 | semidirect |
| 4. #10622727 | C2 | semidirect |
| 5. C2×#66885 | C2 | semidirect |
| 6. #10622461 | C2 | semidirect |
| 7. #10622455 | C2 | semidirect |
| 8. #10622348 | C2 | semidirect |
| 9. #10622344 | C2 | semidirect |
| 10. #10622307 | C2 | semidirect |
| 11. C4×#4314 | C2 | semidirect |
| 14. C22×C8×C11 | C22 | semidirect |
| 18. C2×C4⋊Dic11 | C22 | semidirect |
| 19. #66977 | C22 | semidirect |
| 21. C2×#4314 | C22 | semidirect |
| 28. #66922 | C22 | semidirect |
| 29. C4×Dic22 | 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. #66881 | C22 | semidirect |
| 39. #66881 | C22 | semidirect |
| 40. #66880 | C22 | semidirect |
| 84. D4×C11 | SD16 | semidirect |
| 120. C8×D4 | D11 | semidirect |
| 146. C22×C8 | C2×D11 | semidirect |
| 162. C4⋊C8 | C2×D11 | semidirect |
| 169. C22⋊C8 | C2×D11 | semidirect |
| 170. C4×C8 | C2×D11 | semidirect |
| 213. C11 | #3295 | semidirect |
| 231. D4 | #4314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D44 | 2 |
| #10623074 | 2 |
| C8×D4×C11 | 2 |
| #10622727 | 2 |
| C2×#66885 | 2 |
| #10622461 | 2 |
| #10622455 | 2 |
| #10622348 | 2 |
| #10622344 | 2 |
| #10622307 | 2 |
| C4×#4314 | 2 |
| #3295 | 11 |