Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862271 | C2 | semidirect |
| 2. C22×D1048 | C2 | semidirect |
| 3. #22553876 | C2 | semidirect |
| 4. #22553698 | C2 | semidirect |
| 5. #22553697 | C2 | semidirect |
| 6. #22553687 | C2 | semidirect |
| 7. #22553267 | C2 | semidirect |
| 8. C2×#135×C131 | C2 | semidirect |
| 11. C2×#14523500 | C22 | semidirect |
| 15. C2×#14523498 | C22 | semidirect |
| 17. #16862242 | C22 | semidirect |
| 18. #16862235 | C22 | semidirect |
| 22. #16862156 | C22 | semidirect |
| 23. C8×Dic131 | C22 | semidirect |
| 26. C2×Q16×C131 | C22 | semidirect |
| 27. C2×SD16×C131 | C22 | semidirect |
| 28. C2×D8×C131 | C22 | semidirect |
| 40. #14523497 | D4 | semidirect |
| 56. C2×C8×C131 | D4 | semidirect |
| 101. C131 | #3155 | semidirect |
| 104. C2×#135 | D131 | semidirect |
| 115. C2×Q16 | C2×D131 | semidirect |
| 117. C2×SD16 | C2×D131 | semidirect |
| 122. C2×D8 | C2×D131 | semidirect |
| 154. C2×C8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| C22×D1048 | 2 |
| #22553876 | 2 |
| #22553698 | 2 |
| #22553697 | 2 |
| #22553687 | 2 |
| #22553267 | 2 |
| C2×#135×C131 | 2 |
| #3155 | 131 |