Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 565 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. #22553938 | C2 | direct (N × H) |
| 2. C2×#16862225 | C2 | semidirect |
| 3. C2×#16862223 | C2 | semidirect |
| 6. C22×Dic262 | C22 | semidirect |
| 8. #16862225 | C22 | semidirect |
| 9. #16862223 | C22 | semidirect |
| 10. C2×C4⋊Dic131 | C22 | semidirect |
| 11. C2×Dic131⋊C4 | C22 | semidirect |
| 20. C2×Dic262 | C23 | semidirect |
| 24. C4⋊Dic131 | C23 | semidirect |
| 25. Dic131⋊C4 | C23 | semidirect |
| 29. C24×C131 | Q8 | semidirect |
| 47. C23×C131 | C2×Q8 | semidirect |
| 68. C2×C131 | #543 | semidirect |
| 71. C131 | C2×#543 | semidirect |
| 92. C24 | Dic262 | semidirect |
| 115. C23 | C2×Dic262 | semidirect |
| 140. C2 | #22553938 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553938 | 2 |
| C2×#16862225 | 2 |
| C2×#16862223 | 2 |
| C22×C22⋊Dic131 | 2 |
| C22×C22⋊C4×C131 | 2 |
| C2×#543 | 131 |