Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×Q8×D131 | C2 | semidirect |
| 2. C2×#16862276 | C2 | semidirect |
| 4. #22553466 | C2 | semidirect |
| 5. #22553449 | C2 | semidirect |
| 6. #22553322 | C2 | semidirect |
| 7. #22553321 | C2 | semidirect |
| 8. #22553275 | C2 | semidirect |
| 9. C2×#137×C131 | C2 | semidirect |
| 19. C2×#14523503 | C22 | semidirect |
| 20. C2×#14523501 | C22 | semidirect |
| 28. #16862171 | C22 | semidirect |
| 29. #16862170 | C22 | semidirect |
| 34. C2×Q16×C131 | C22 | semidirect |
| 35. C2×SD16×C131 | C22 | semidirect |
| 42. C2×Dic262 | D4 | semidirect |
| 70. C2×Q8×C131 | D4 | semidirect |
| 127. C2×D131 | #137 | semidirect |
| 141. C131 | #3004 | semidirect |
| 145. C2×#137 | D131 | semidirect |
| 165. C2×Q16 | C2×D131 | semidirect |
| 167. C2×SD16 | C2×D131 | semidirect |
| 193. C2×Q8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D131 | 2 |
| C2×#16862276 | 2 |
| #22553819 | 2 |
| #22553466 | 2 |
| #22553449 | 2 |
| #22553322 | 2 |
| #22553321 | 2 |
| #22553275 | 2 |
| C2×#137×C131 | 2 |
| #3004 | 131 |