Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×#16862254 | C2 | semidirect |
| 2. #22553890 | C2 | semidirect |
| 3. #22553879 | C2 | semidirect |
| 4. #22553562 | C2 | semidirect |
| 5. #22553555 | C2 | semidirect |
| 6. #22553545 | C2 | semidirect |
| 7. #22553538 | C2 | semidirect |
| 8. #22553354 | C2 | semidirect |
| 9. #22553308 | C2 | semidirect |
| 10. C2×#16862167 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C131 | C2 | semidirect |
| 14. C2×#14523496 | C22 | semidirect |
| 16. C2×C8×D131 | C22 | semidirect |
| 20. #16862222 | C22 | semidirect |
| 25. #16862217 | C22 | semidirect |
| 29. #16862180 | C22 | semidirect |
| 30. #16862178 | C22 | semidirect |
| 31. #16862170 | C22 | semidirect |
| 32. #16862170 | C22 | semidirect |
| 35. #16862167 | C22 | semidirect |
| 36. #16862167 | C22 | semidirect |
| 83. M16×C131 | D4 | semidirect |
| 151. C131 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D131 | semidirect |
| 220. M16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862254 | 2 |
| #22553890 | 2 |
| #22553879 | 2 |
| #22553562 | 2 |
| #22553555 | 2 |
| #22553545 | 2 |
| #22553538 | 2 |
| #22553354 | 2 |
| #22553308 | 2 |
| C2×#16862167 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| #3062 | 131 |