Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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×D2096 | C2 | semidirect |
| 2. C2×#16862187 | C2 | semidirect |
| 3. #22553687 | C2 | semidirect |
| 4. C16×Dic131 | C2 | semidirect |
| 5. C2×D16×C131 | C2 | semidirect |
| 23. C131⋊C16 | D4 | semidirect |
| 28. C16×C131 | D4 | semidirect |
| 48. Dic131 | D16 | semidirect |
| 53. C131 | #2246 | semidirect |
| 57. C2×D16 | D131 | semidirect |
| 82. C16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2096 | 2 |
| C2×#16862187 | 2 |
| #22553687 | 2 |
| C16×Dic131 | 2 |
| C2×D16×C131 | 2 |
| #2246 | 131 |