Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×#16862272 | C2 | semidirect |
| 2. #22553858 | C2 | semidirect |
| 3. C2×D4×Dic131 | C2 | semidirect |
| 4. #22553529 | C2 | semidirect |
| 5. #22553525 | C2 | semidirect |
| 6. #22553515 | C2 | semidirect |
| 7. #22553505 | C2 | semidirect |
| 8. #22553335 | C2 | semidirect |
| 9. #22553314 | C2 | semidirect |
| 10. #22553313 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C131 | C2 | semidirect |
| 18. #16862244 | C22 | semidirect |
| 19. #16862242 | C22 | semidirect |
| 20. #16862235 | C22 | semidirect |
| 21. #16862233 | C22 | semidirect |
| 33. Dic131⋊C8 | C22 | semidirect |
| 34. Dic131⋊C8 | C22 | semidirect |
| 35. #16862171 | C22 | semidirect |
| 36. #16862170 | C22 | semidirect |
| 37. #16862168 | C22 | semidirect |
| 38. #16862167 | C22 | semidirect |
| 84. C2×D4×C131 | D4 | semidirect |
| 158. Dic131 | AGL(1,ℤ/8) | semidirect |
| 166. C131 | #3036 | semidirect |
| 169. C2×AGL(1,ℤ/8) | D131 | semidirect |
| 226. C2×D4 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862272 | 2 |
| #22553858 | 2 |
| C2×D4×Dic131 | 2 |
| #22553529 | 2 |
| #22553525 | 2 |
| #22553515 | 2 |
| #22553505 | 2 |
| #22553335 | 2 |
| #22553314 | 2 |
| #22553313 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| #3036 | 131 |