Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
656 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 357 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 |
|---|---|---|
| 3. C4×#14523496 | C2 | direct (N × H) |
| 4. C2×#16862156 | C2 | semidirect |
| 5. C2×C4×C131⋊C8 | C2 | semidirect |
| 6. C2×C4×C8×C131 | C2 | semidirect |
| 9. C2×#14523496 | C4 | direct (N × H) |
| 16. #16862156 | C22 | semidirect |
| 17. C4×C131⋊C8 | C22 | semidirect |
| 20. C4×C8×C131 | C22 | semidirect |
| 29. #14523496 | C2×C4 | direct (N × H) |
| 30. C2×C131⋊C8 | C2×C4 | semidirect |
| 37. C2×C8×C131 | C2×C4 | semidirect |
| 51. C131⋊C8 | C22×C4 | semidirect |
| 53. C2×C4×C131 | M16 | semidirect |
| 58. C8×C131 | C22×C4 | semidirect |
| 66. C4×C131 | C2×M16 | semidirect |
| 70. C2×C131 | C4×M16 | semidirect |
| 74. C131 | C2×C4×M16 | semidirect |
| 81. C2×C4×C8 | D131 | semidirect |
| 95. C4×C8 | C2×D131 | semidirect |
| 109. C2×C8 | C4×D131 | semidirect |
| 127. C2×C4 | #14523496 | direct (N × H) |
| 133. C8 | C2×C4×D131 | semidirect |
| 143. C4 | C2×#14523496 | direct (N × H) |
| 146. C2 | C4×#14523496 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523496 | 2 |
| C2×C42×D131 | 2 |
| C4×#14523496 | 2 |
| C2×#16862156 | 2 |
| C2×C4×C131⋊C8 | 2 |
| C2×C4×C8×C131 | 2 |
| C2×C4×M16 | 131 |