Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
| 2. C2×M16×D131 | C2 | semidirect |
| 4. C2×#16862222 | C2 | semidirect |
| 5. #22553569 | C2 | semidirect |
| 6. #22553561 | C2 | semidirect |
| 7. #22553552 | C2 | semidirect |
| 8. #22553544 | C2 | semidirect |
| 9. #22553355 | C2 | semidirect |
| 10. #22553314 | C2 | semidirect |
| 11. #419×C131 | C2 | semidirect |
| 15. C2×#14523503 | C22 | semidirect |
| 16. C2×#14523500 | C22 | semidirect |
| 36. #16862179 | C22 | semidirect |
| 37. #16862177 | C22 | semidirect |
| 38. #16862171 | C22 | semidirect |
| 39. #16862168 | C22 | semidirect |
| 43. #103×C131 | C22 | semidirect |
| 44. #103×C131 | C22 | semidirect |
| 64. #14523497 | D4 | semidirect |
| 145. C2×D131 | #137 | semidirect |
| 163. C131 | #3056 | semidirect |
| 174. #419 | D131 | semidirect |
| 206. #103 | C2×D131 | semidirect |
| 207. #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×M16×D131 | 2 |
| #22553824 | 2 |
| C2×#16862222 | 2 |
| #22553569 | 2 |
| #22553561 | 2 |
| #22553552 | 2 |
| #22553544 | 2 |
| #22553355 | 2 |
| #22553314 | 2 |
| #419×C131 | 2 |
| #3056 | 131 |