Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D131 | C2 | semidirect |
| 3. C2×#16862174 | C2 | semidirect |
| 4. C2×#16862172 | C2 | semidirect |
| 5. C4×(C2×D131)⋊C4 | C2 | semidirect |
| 6. #22553071 | C2 | semidirect |
| 7. #339×C131 | C2 | semidirect |
| 16. #16862226 | C4 | semidirect |
| 17. #16862226 | C4 | semidirect |
| 18. #16862221 | C4 | semidirect |
| 19. #16862221 | C4 | semidirect |
| 53. #14523497 | D4 | semidirect |
| 69. M16×C131 | D4 | semidirect |
| 139. C2×D131 | #104 | semidirect |
| 159. C131 | #1871 | semidirect |
| 167. #339 | D131 | semidirect |
| 218. M16 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D131 | 2 |
| #22553824 | 2 |
| C2×#16862174 | 2 |
| C2×#16862172 | 2 |
| C4×(C2×D131)⋊C4 | 2 |
| #22553071 | 2 |
| #339×C131 | 2 |
| #1871 | 131 |