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×#16862266 | C2 | direct (N × H) |
| 3. C22×#14523503 | C2 | semidirect |
| 4. C22×#14523501 | C2 | semidirect |
| 5. C22×#14523500 | C2 | semidirect |
| 6. C22×#14523498 | C2 | semidirect |
| 7. C23×C131⋊C8 | C2 | semidirect |
| 8. C22×#41×C131 | C2 | semidirect |
| 10. C2×#14523513 | C22 | semidirect |
| 15. #16862266 | C22 | direct (N × H) |
| 16. C2×#14523503 | C22 | semidirect |
| 17. C2×#14523501 | C22 | semidirect |
| 18. C2×#14523500 | C22 | semidirect |
| 19. C2×#14523498 | C22 | semidirect |
| 22. C22×C131⋊C8 | C22 | semidirect |
| 24. C2×#41×C131 | C22 | semidirect |
| 32. #14523513 | C23 | semidirect |
| 40. #14523503 | C23 | semidirect |
| 41. #14523501 | C23 | semidirect |
| 42. #14523500 | C23 | semidirect |
| 43. #14523498 | C23 | semidirect |
| 46. C2×C131⋊C8 | C23 | semidirect |
| 50. #41×C131 | C23 | semidirect |
| 93. C22×C131 | #135 | semidirect |
| 105. C2×C131 | C2×#135 | semidirect |
| 108. C131 | C22×#135 | semidirect |
| 111. C22×#41 | D131 | semidirect |
| 121. C2×#41 | C2×D131 | semidirect |
| 145. #41 | C22×D131 | semidirect |
| 204. C22 | #16862266 | direct (N × H) |
| 215. C2 | C2×#16862266 | 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×#16862266 | 2 |
| C22×#14523503 | 2 |
| C22×#14523501 | 2 |
| C22×#14523500 | 2 |
| C22×#14523498 | 2 |
| C23×C131⋊C8 | 2 |
| C22×#41×C131 | 2 |
| C22×#135 | 131 |