Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1976 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 645 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. C23×D524 | C2 | semidirect |
| 2. C22×#14523498 | C2 | direct (N × H) |
| 3. C23×C131⋊C8 | C2 | semidirect |
| 4. C23×D4×C131 | C2 | semidirect |
| 7. C22×D524 | C22 | semidirect |
| 8. C2×#14523498 | C22 | direct (N × H) |
| 9. C22×C131⋊C8 | C22 | semidirect |
| 12. C22×D4×C131 | C22 | semidirect |
| 17. C2×D524 | C23 | semidirect |
| 18. #14523498 | C23 | direct (N × H) |
| 19. C2×C131⋊C8 | C23 | semidirect |
| 24. C2×D4×C131 | C23 | semidirect |
| 30. D524 | C24 | semidirect |
| 31. C131⋊C8 | C24 | semidirect |
| 34. C23×C131 | D8 | semidirect |
| 37. D4×C131 | C24 | semidirect |
| 42. C22×C131 | C2×D8 | semidirect |
| 49. C2×C131 | C22×D8 | semidirect |
| 52. C131 | C23×D8 | semidirect |
| 55. C23×D4 | D131 | semidirect |
| 63. C22×D4 | C2×D131 | semidirect |
| 75. C2×D4 | C22×D131 | semidirect |
| 84. C23 | #14523498 | direct (N × H) |
| 89. D4 | C23×D131 | semidirect |
| 97. C22 | C2×#14523498 | direct (N × H) |
| 103. C2 | C22×#14523498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D524 | 2 |
| C22×#14523498 | 2 |
| C23×C131⋊C8 | 2 |
| C23×D4×C131 | 2 |
| C23×D8 | 131 |