Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #22553924 | C2 | direct (N × H) |
| 2. C2×#16862246 | C2 | semidirect |
| 4. C2×#16862238 | C2 | semidirect |
| 5. C2×#16862236 | C2 | semidirect |
| 7. C2×C4×Dic262 | C2 | semidirect |
| 10. #16862246 | C22 | semidirect |
| 12. #16862238 | C22 | semidirect |
| 13. #16862236 | C22 | semidirect |
| 15. C4×Dic262 | C22 | semidirect |
| 82. C2×C131 | #541 | semidirect |
| 85. C131 | C2×#541 | semidirect |
| 168. C2 | #22553924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553924 | 2 |
| C2×#16862246 | 2 |
| C2×#16862239 | 2 |
| C2×#16862238 | 2 |
| C2×#16862236 | 2 |
| C2×#16862225 | 2 |
| C2×C4×Dic262 | 2 |
| C2×#117×C131 | 2 |
| C2×#541 | 131 |