Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1968 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 645 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. C24×Dic131 | C2 | semidirect |
| 2. C2×#16862227 | C2 | direct (N × H) |
| 3. C22×Dic131⋊C4 | C2 | semidirect |
| 4. C22×C22⋊Dic131 | C2 | semidirect |
| 5. C22×C22⋊Dic131 | C2 | semidirect |
| 10. C23×Dic131 | C22 | semidirect |
| 11. #16862227 | C22 | direct (N × H) |
| 12. C2×Dic131⋊C4 | C22 | semidirect |
| 13. C2×C22⋊Dic131 | C22 | semidirect |
| 14. C2×C22⋊Dic131 | C22 | semidirect |
| 25. C22×Dic131 | C23 | semidirect |
| 26. Dic131⋊C4 | C23 | semidirect |
| 27. C22⋊Dic131 | C23 | semidirect |
| 28. C22⋊Dic131 | C23 | semidirect |
| 64. C22×C131 | #123 | semidirect |
| 74. C2×C131 | C2×#123 | semidirect |
| 77. C131 | C22×#123 | semidirect |
| 142. C22 | #16862227 | direct (N × H) |
| 152. C2 | C2×#16862227 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic131 | 2 |
| C2×#16862227 | 2 |
| C22×Dic131⋊C4 | 2 |
| C22×C22⋊Dic131 | 2 |
| C23×D4×C131 | 2 |
| C22×#123 | 131 |