Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862277 | C2 | semidirect |
| 2. C2×#16862253 | C2 | semidirect |
| 4. #22553568 | C2 | semidirect |
| 5. #22553560 | C2 | semidirect |
| 6. #22553551 | C2 | semidirect |
| 7. #22553543 | C2 | semidirect |
| 8. #22553355 | C2 | semidirect |
| 9. #22553306 | C2 | semidirect |
| 10. C2×#16862170 | C2 | semidirect |
| 11. #536×C131 | C2 | semidirect |
| 54. #14523497 | D4 | semidirect |
| 143. C131 | #3063 | semidirect |
| 148. #536 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| C2×#16862253 | 2 |
| #22553890 | 2 |
| #22553568 | 2 |
| #22553560 | 2 |
| #22553551 | 2 |
| #22553543 | 2 |
| #22553355 | 2 |
| #22553306 | 2 |
| C2×#16862170 | 2 |
| #536×C131 | 2 |
| #3063 | 131 |