Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16862269 | C2 | semidirect |
| 2. C2×#16862267 | C2 | semidirect |
| 3. #22553863 | C2 | semidirect |
| 4. #22553861 | C2 | semidirect |
| 5. #22553705 | C2 | semidirect |
| 6. #22553704 | C2 | semidirect |
| 7. #22553702 | C2 | semidirect |
| 8. #22553701 | C2 | semidirect |
| 9. #22553698 | C2 | semidirect |
| 10. #97×D131 | C2 | semidirect |
| 11. #497×C131 | C2 | semidirect |
| 65. C8×D131 | D4 | semidirect |
| 133. C131 | #3150 | semidirect |
| 141. #497 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862269 | 2 |
| C2×#16862267 | 2 |
| #22553863 | 2 |
| #22553861 | 2 |
| #22553705 | 2 |
| #22553704 | 2 |
| #22553702 | 2 |
| #22553701 | 2 |
| #22553698 | 2 |
| #97×D131 | 2 |
| #497×C131 | 2 |
| #3150 | 131 |