Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1504 conjugacy classes of subgroups; only the 821 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 821 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 |
|---|---|---|
| 2. C2×#16862254 | C2 | direct (N × H) |
| 3. C22×#14523496 | C2 | semidirect |
| 4. C23×C131⋊C8 | C2 | semidirect |
| 5. C22×C8×D131 | C2 | semidirect |
| 6. C22×M16×C131 | C2 | semidirect |
| 13. #16862254 | C22 | direct (N × H) |
| 14. C2×#14523496 | C22 | semidirect |
| 17. C22×C131⋊C8 | C22 | semidirect |
| 18. C2×C8×D131 | C22 | semidirect |
| 20. C2×M16×C131 | C22 | semidirect |
| 31. #14523496 | C23 | semidirect |
| 34. C2×C131⋊C8 | C23 | semidirect |
| 35. C8×D131 | C23 | semidirect |
| 41. M16×C131 | C23 | semidirect |
| 63. C22×C131 | #131 | semidirect |
| 73. C2×C131 | C2×#131 | semidirect |
| 76. C131 | C22×#131 | semidirect |
| 81. C22×M16 | D131 | semidirect |
| 93. C2×M16 | C2×D131 | semidirect |
| 114. M16 | C22×D131 | semidirect |
| 142. C22 | #16862254 | direct (N × H) |
| 151. C2 | C2×#16862254 | 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×#16862254 | 2 |
| C22×#14523496 | 2 |
| C23×C131⋊C8 | 2 |
| C22×C8×D131 | 2 |
| C22×M16×C131 | 2 |
| C22×#131 | 131 |