Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#16862265 | C2 | semidirect |
| 2. C2×#16862252 | C2 | semidirect |
| 3. #22553891 | C2 | semidirect |
| 4. #22553557 | C2 | semidirect |
| 5. #22553556 | C2 | semidirect |
| 6. #22553554 | C2 | semidirect |
| 7. #22553553 | C2 | semidirect |
| 8. #22553545 | C2 | semidirect |
| 9. #107×D131 | C2 | semidirect |
| 10. #22553310 | C2 | semidirect |
| 11. #466×C131 | C2 | semidirect |
| 64. C8×D131 | D4 | semidirect |
| 143. C131 | #3061 | semidirect |
| 153. #466 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862265 | 2 |
| C2×#16862252 | 2 |
| #22553891 | 2 |
| #22553557 | 2 |
| #22553556 | 2 |
| #22553554 | 2 |
| #22553553 | 2 |
| #22553545 | 2 |
| #107×D131 | 2 |
| #22553310 | 2 |
| #466×C131 | 2 |
| #3061 | 131 |