Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #22553789 | C2 | semidirect |
| 3. #22553412 | C2 | semidirect |
| 4. C4×#14523501 | C2 | semidirect |
| 5. #22553348 | C2 | semidirect |
| 6. #22553320 | C2 | semidirect |
| 8. #22553268 | C2 | semidirect |
| 11. C2×#14523501 | C4 | semidirect |
| 16. C4×Dic262 | C22 | semidirect |
| 20. #16862179 | C22 | semidirect |
| 21. #16862177 | C22 | semidirect |
| 22. #16862169 | C22 | semidirect |
| 24. #16862157 | C22 | semidirect |
| 25. C4×C131⋊C8 | C22 | semidirect |
| 34. C2×Dic262 | C2×C4 | semidirect |
| 37. #14523501 | C2×C4 | semidirect |
| 38. #14523501 | C2×C4 | semidirect |
| 40. C2×C131⋊C8 | C2×C4 | semidirect |
| 103. C131 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523501 | 2 |
| #22553789 | 2 |
| #22553412 | 2 |
| C4×#14523501 | 2 |
| #22553348 | 2 |
| #22553320 | 2 |
| #22553317 | 2 |
| #22553268 | 2 |
| #518×C131 | 2 |
| #2949 | 131 |