Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 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×D1048 | C2 | semidirect |
| 2. #22553876 | C2 | semidirect |
| 3. #22553565 | C2 | semidirect |
| 4. #22553548 | C2 | semidirect |
| 5. #22553350 | C2 | semidirect |
| 6. #22553318 | C2 | semidirect |
| 7. C2×#131×C131 | C2 | semidirect |
| 14. #16862220 | C22 | semidirect |
| 17. #16862180 | C22 | semidirect |
| 18. #16862178 | C22 | semidirect |
| 19. #16862168 | C22 | semidirect |
| 23. C2×M16×C131 | C22 | semidirect |
| 25. C22×C8×C131 | C22 | semidirect |
| 48. C2×C8×C131 | D4 | semidirect |
| 93. C131 | #3058 | semidirect |
| 96. C2×#131 | D131 | semidirect |
| 109. C2×M16 | C2×D131 | semidirect |
| 111. C22×C8 | C2×D131 | semidirect |
| 138. C2×C8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1048 | 2 |
| #22553876 | 2 |
| #22553565 | 2 |
| #22553548 | 2 |
| #22553350 | 2 |
| #22553318 | 2 |
| C2×#131×C131 | 2 |
| #3058 | 131 |