Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
760 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 197 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×#14523498 | C2 | semidirect |
| 2. C2×#16862243 | C2 | semidirect |
| 3. #22553688 | C2 | direct (N × H) |
| 4. C2×C4×C131⋊C8 | C2 | semidirect |
| 5. C2×#127×C131 | C2 | semidirect |
| 9. C2×#14523498 | C22 | semidirect |
| 12. #16862243 | C22 | semidirect |
| 13. C4×C131⋊C8 | C22 | semidirect |
| 17. #127×C131 | C22 | semidirect |
| 26. C2×C131⋊C8 | D4 | semidirect |
| 44. C131⋊C8 | C2×D4 | semidirect |
| 52. C2×C4×C131 | D8 | semidirect |
| 67. C4×C131 | C2×D8 | semidirect |
| 70. C2×C131 | #493 | semidirect |
| 74. C131 | C2×#493 | semidirect |
| 78. C2×#127 | D131 | semidirect |
| 91. #127 | C2×D131 | semidirect |
| 126. C2×C4 | #14523498 | semidirect |
| 142. C4 | C2×#14523498 | semidirect |
| 146. C2 | #22553688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523498 | 2 |
| C2×#16862243 | 2 |
| #22553688 | 2 |
| C2×C4×C131⋊C8 | 2 |
| C2×#127×C131 | 2 |
| C2×#493 | 131 |