Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862237 | C2 | semidirect |
| 3. #22553615 | C2 | direct (N × H) |
| 4. C2×#16862177 | C2 | semidirect |
| 5. C2×Dic131⋊C8 | C2 | semidirect |
| 8. C2×#107×C131 | C2 | semidirect |
| 13. #16862237 | C22 | semidirect |
| 21. #16862177 | C22 | semidirect |
| 22. Dic131⋊C8 | C22 | semidirect |
| 28. #107×C131 | C22 | semidirect |
| 98. C2×C131 | #478 | semidirect |
| 103. C131 | C2×#478 | semidirect |
| 108. C2×#107 | D131 | semidirect |
| 128. #107 | C2×D131 | semidirect |
| 203. C2 | #22553615 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862237 | 2 |
| C2×#16862208 | 2 |
| #22553615 | 2 |
| C2×#16862177 | 2 |
| C2×Dic131⋊C8 | 2 |
| C2×#16862168 | 2 |
| C2×#16862166 | 2 |
| C2×#107×C131 | 2 |
| C2×#478 | 131 |