Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 565 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×#14523513 | C2 | semidirect |
| 2. C2×#16862268 | C2 | direct (N × H) |
| 3. C22×Dic524 | C2 | semidirect |
| 4. C22×#14523502 | C2 | semidirect |
| 5. C22×D1048 | C2 | semidirect |
| 6. C23×C8×C131 | C2 | semidirect |
| 8. C2×#14523513 | C22 | semidirect |
| 13. #16862268 | C22 | direct (N × H) |
| 14. C2×Dic524 | C22 | semidirect |
| 15. C2×#14523502 | C22 | semidirect |
| 16. C2×D1048 | C22 | semidirect |
| 20. C22×C8×C131 | C22 | semidirect |
| 23. #14523513 | C23 | semidirect |
| 31. Dic524 | C23 | semidirect |
| 32. #14523502 | C23 | semidirect |
| 33. D1048 | C23 | semidirect |
| 41. C2×C8×C131 | C23 | semidirect |
| 62. C22×C131 | #135 | semidirect |
| 72. C2×C131 | C2×#135 | semidirect |
| 75. C131 | C22×#135 | semidirect |
| 82. C23×C8 | D131 | semidirect |
| 96. C22×C8 | C2×D131 | semidirect |
| 117. C2×C8 | C22×D131 | semidirect |
| 140. C22 | #16862268 | direct (N × H) |
| 149. C2 | C2×#16862268 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523513 | 2 |
| C2×#16862268 | 2 |
| C22×Dic524 | 2 |
| C22×#14523502 | 2 |
| C22×D1048 | 2 |
| C23×C8×C131 | 2 |
| C22×#135 | 131 |