Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #22553353 | C2 | semidirect |
| 4. #22553351 | C2 | semidirect |
| 5. #22553350 | C2 | semidirect |
| 6. #22553348 | C2 | semidirect |
| 7. #427×C131 | C2 | semidirect |
| 9. C2×#14523496 | C4 | semidirect |
| 20. #16862180 | C22 | semidirect |
| 21. #16862179 | C22 | semidirect |
| 22. #16862178 | C22 | semidirect |
| 23. #16862177 | C22 | semidirect |
| 26. #107×C131 | C22 | semidirect |
| 27. #106×C131 | C22 | semidirect |
| 35. #14523496 | C2×C4 | semidirect |
| 36. #14523496 | C2×C4 | semidirect |
| 37. C2×C131⋊C8 | C2×C4 | semidirect |
| 46. C2×C8×C131 | C2×C4 | semidirect |
| 87. C131 | #2911 | semidirect |
| 95. #427 | D131 | semidirect |
| 112. #107 | C2×D131 | semidirect |
| 115. #106 | C2×D131 | semidirect |
| 128. C2×C8 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523496 | 2 |
| #117×D131 | 2 |
| #22553353 | 2 |
| #22553351 | 2 |
| #22553350 | 2 |
| #22553348 | 2 |
| #427×C131 | 2 |
| #2911 | 131 |