Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14523498 | C2 | semidirect |
| 2. C23×C131⋊C8 | C2 | semidirect |
| 3. C2×#16862220 | C2 | semidirect |
| 4. #22553546 | C2 | direct (N × H) |
| 5. C2×#16862179 | C2 | semidirect |
| 6. C2×#16862167 | C2 | semidirect |
| 7. C2×#16862166 | C2 | semidirect |
| 8. C2×#121×C131 | C2 | semidirect |
| 12. C2×#14523498 | C22 | semidirect |
| 16. C22×C131⋊C8 | C22 | semidirect |
| 18. #16862220 | C22 | semidirect |
| 21. #16862179 | C22 | semidirect |
| 22. #16862167 | C22 | semidirect |
| 23. #16862166 | C22 | semidirect |
| 28. #121×C131 | C22 | semidirect |
| 42. C2×C131⋊C8 | D4 | semidirect |
| 77. C131⋊C8 | C2×D4 | semidirect |
| 84. C23×C131 | D8 | semidirect |
| 111. C22×C131 | C2×D8 | semidirect |
| 126. C2×C131 | #466 | semidirect |
| 131. C131 | C2×#466 | semidirect |
| 136. C2×#121 | D131 | semidirect |
| 155. #121 | C2×D131 | semidirect |
| 208. C23 | #14523498 | semidirect |
| 247. C22 | C2×#14523498 | semidirect |
| 259. C2 | #22553546 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523498 | 2 |
| C23×C131⋊C8 | 2 |
| C2×#16862220 | 2 |
| #22553546 | 2 |
| C2×#16862179 | 2 |
| C2×#16862167 | 2 |
| C2×#16862166 | 2 |
| C2×#121×C131 | 2 |
| C2×#466 | 131 |