Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 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×#14523501 | C2 | semidirect |
| 2. C2×#16862246 | C2 | semidirect |
| 3. #22553684 | C2 | direct (N × H) |
| 4. C2×C4×C131⋊C8 | C2 | semidirect |
| 8. C2×#14523501 | C22 | semidirect |
| 11. #16862246 | C22 | semidirect |
| 13. C4×C131⋊C8 | C22 | semidirect |
| 24. C2×C131⋊C8 | D4 | semidirect |
| 41. C131⋊C8 | C2×D4 | semidirect |
| 49. C2×C4×C131 | SD16 | semidirect |
| 61. C4×C131 | C2×SD16 | semidirect |
| 65. C2×C131 | #492 | semidirect |
| 68. C131 | C2×#492 | semidirect |
| 117. C2×C4 | #14523501 | semidirect |
| 131. C4 | C2×#14523501 | semidirect |
| 134. C2 | #22553684 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523501 | 2 |
| C2×#16862246 | 2 |
| #22553684 | 2 |
| C2×C4×C131⋊C8 | 2 |
| C2×#127×C131 | 2 |
| C2×#492 | 131 |