Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22554117 | C2 | semidirect |
| 2. #22553750 | C2 | semidirect |
| 3. #22553744 | C2 | semidirect |
| 4. C2×D2096 | C2 | semidirect |
| 5. #504×C131 | C2 | semidirect |
| 8. #16862268 | C22 | semidirect |
| 9. C2×D1048 | C22 | semidirect |
| 10. Dic1048 | C22 | semidirect |
| 11. #16862191 | C22 | semidirect |
| 12. D2096 | C22 | semidirect |
| 13. D2096 | C22 | semidirect |
| 15. M32×C131 | C22 | semidirect |
| 16. C2×C16×C131 | C22 | semidirect |
| 50. C131 | #3415 | semidirect |
| 56. #504 | D131 | semidirect |
| 66. M32 | C2×D131 | semidirect |
| 67. C2×C16 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554117 | 2 |
| #22553750 | 2 |
| #22553744 | 2 |
| C2×D2096 | 2 |
| #504×C131 | 2 |
| #3415 | 131 |