Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14523502 | C2 | semidirect |
| 2. C2×#16862225 | C2 | semidirect |
| 4. #22553558 | C2 | direct (N × H) |
| 5. C2×#16862180 | C2 | semidirect |
| 6. C2×#16862171 | C2 | semidirect |
| 7. C2×#16862168 | C2 | semidirect |
| 8. C22×M16×C131 | C2 | semidirect |
| 13. C2×#14523502 | C22 | semidirect |
| 15. #16862225 | C22 | semidirect |
| 23. #16862180 | C22 | semidirect |
| 24. #16862171 | C22 | semidirect |
| 25. #16862168 | C22 | semidirect |
| 28. C2×M16×C131 | C22 | semidirect |
| 62. C2×C8×C131 | D4 | semidirect |
| 97. C8×C131 | C2×D4 | semidirect |
| 118. C2×C131 | #468 | semidirect |
| 123. C131 | C2×#468 | semidirect |
| 126. C22×M16 | D131 | semidirect |
| 140. C2×M16 | C2×D131 | semidirect |
| 179. C2×C8 | C22⋊D131 | semidirect |
| 221. C8 | C2×C22⋊D131 | semidirect |
| 243. C2 | #22553558 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523502 | 2 |
| C2×#16862225 | 2 |
| C2×#16862220 | 2 |
| #22553558 | 2 |
| C2×#16862180 | 2 |
| C2×#16862171 | 2 |
| C2×#16862168 | 2 |
| C22×M16×C131 | 2 |
| C2×#468 | 131 |