Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16862277 | C2 | semidirect |
| 3. C2×#16862235 | C2 | semidirect |
| 4. #22553780 | C2 | semidirect |
| 5. #22553537 | C2 | semidirect |
| 6. #22553530 | C2 | semidirect |
| 7. #22553335 | C2 | semidirect |
| 8. #22553316 | C2 | semidirect |
| 9. #419×C131 | C2 | semidirect |
| 14. C2×#14523503 | C22 | semidirect |
| 16. C2×#14523500 | C22 | semidirect |
| 22. #16862211 | C22 | semidirect |
| 23. #16862208 | C22 | semidirect |
| 29. Dic131⋊C8 | C22 | semidirect |
| 34. #103×C131 | C22 | semidirect |
| 125. C131 | #3040 | semidirect |
| 134. #419 | D131 | semidirect |
| 159. #103 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| C2×#16862274 | 2 |
| C2×#16862235 | 2 |
| #22553780 | 2 |
| #22553537 | 2 |
| #22553530 | 2 |
| #22553335 | 2 |
| #22553316 | 2 |
| #419×C131 | 2 |
| #3040 | 131 |