Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1504 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 1077 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. C2×#16862253 | C2 | direct (N × H) |
| 2. C22×#14523497 | C2 | semidirect |
| 3. C23×C131⋊C8 | C2 | semidirect |
| 5. #16862253 | C22 | direct (N × H) |
| 6. C2×#14523497 | C22 | semidirect |
| 9. C22×C131⋊C8 | C22 | semidirect |
| 15. #14523497 | C23 | semidirect |
| 18. C2×C131⋊C8 | C23 | semidirect |
| 41. C22×C131 | #131 | semidirect |
| 48. C2×C131 | C2×#131 | semidirect |
| 50. C131 | C22×#131 | semidirect |
| 92. C22 | #16862253 | direct (N × H) |
| 99. C2 | C2×#16862253 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862253 | 2 |
| C22×#14523497 | 2 |
| C23×C131⋊C8 | 2 |
| C22×#41×C131 | 2 |
| C22×#131 | 131 |