Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862271 | C2 | semidirect |
| 2. C22×#14523498 | C2 | semidirect |
| 3. C2×#16862253 | C2 | semidirect |
| 4. #22553580 | C2 | direct (N × H) |
| 5. C2×#16862181 | C2 | semidirect |
| 6. C2×#16862163 | C2 | semidirect |
| 7. C2×#16862162 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C131 | C2 | semidirect |
| 11. #16862271 | C22 | semidirect |
| 17. C2×#14523498 | C22 | semidirect |
| 19. #16862253 | C22 | semidirect |
| 25. #16862181 | C22 | semidirect |
| 26. #16862163 | C22 | semidirect |
| 27. #16862162 | C22 | semidirect |
| 31. AGL(1,ℤ/8)×C131 | C22 | semidirect |
| 140. C2×C131 | #472 | semidirect |
| 143. C131 | C2×#472 | semidirect |
| 146. C2×AGL(1,ℤ/8) | D131 | semidirect |
| 159. AGL(1,ℤ/8) | C2×D131 | semidirect |
| 285. C2 | #22553580 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| C22×#14523498 | 2 |
| C2×#16862253 | 2 |
| #22553580 | 2 |
| C2×#16862181 | 2 |
| C2×#16862163 | 2 |
| C2×#16862162 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| C2×#472 | 131 |