Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D131 | C2 | semidirect |
| 3. C2×#16862222 | C2 | semidirect |
| 4. #22553567 | C2 | semidirect |
| 5. #22553555 | C2 | semidirect |
| 6. #22553550 | C2 | semidirect |
| 7. #22553538 | C2 | semidirect |
| 8. #22553354 | C2 | semidirect |
| 9. #22553321 | C2 | semidirect |
| 10. #22553313 | C2 | semidirect |
| 11. C2×#137×C131 | C2 | semidirect |
| 33. #16862180 | C22 | semidirect |
| 34. #16862178 | C22 | semidirect |
| 35. #16862170 | C22 | semidirect |
| 36. #16862170 | C22 | semidirect |
| 37. #16862170 | C22 | semidirect |
| 38. #16862167 | C22 | semidirect |
| 42. C2×Q16×C131 | C22 | semidirect |
| 43. C2×SD16×C131 | C22 | semidirect |
| 90. M16×C131 | D4 | semidirect |
| 145. C2×D131 | #137 | semidirect |
| 163. C131 | #3056 | semidirect |
| 165. C2×#137 | D131 | semidirect |
| 180. C2×Q16 | C2×D131 | semidirect |
| 181. C2×SD16 | C2×D131 | semidirect |
| 236. M16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D131 | 2 |
| #22553819 | 2 |
| C2×#16862222 | 2 |
| #22553567 | 2 |
| #22553555 | 2 |
| #22553550 | 2 |
| #22553538 | 2 |
| #22553354 | 2 |
| #22553321 | 2 |
| #22553313 | 2 |
| C2×#137×C131 | 2 |
| #3056 | 131 |