Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 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×#16862276 | C2 | semidirect |
| 2. C2×#16862276 | C2 | semidirect |
| 3. #22554079 | C2 | semidirect |
| 4. #22553585 | C2 | semidirect |
| 5. #22553573 | C2 | semidirect |
| 6. #22553360 | C2 | semidirect |
| 7. #22553296 | C2 | semidirect |
| 8. C2×#16862164 | C2 | semidirect |
| 16. C2×#14523503 | C22 | semidirect |
| 18. C2×#14523501 | C22 | semidirect |
| 25. #16862181 | C22 | semidirect |
| 26. #16862165 | C22 | semidirect |
| 27. #16862164 | C22 | semidirect |
| 28. #16862163 | C22 | semidirect |
| 142. C131 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862276 | 2 |
| #22554079 | 2 |
| #22553585 | 2 |
| #22553573 | 2 |
| #22553360 | 2 |
| #22553296 | 2 |
| C2×#16862164 | 2 |
| #575×C131 | 2 |
| #3069 | 131 |