Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4×D524 | C2 | semidirect |
| 2. #22553623 | C2 | semidirect |
| 3. #22553589 | C2 | semidirect |
| 4. #22553504 | C2 | semidirect |
| 5. #22553445 | C2 | semidirect |
| 6. C4×#14523498 | C2 | semidirect |
| 7. #22553365 | C2 | semidirect |
| 8. #532×C131 | C2 | semidirect |
| 18. #16862179 | C22 | semidirect |
| 19. C4⋊(C131⋊C8) | C22 | semidirect |
| 20. #16862167 | C22 | semidirect |
| 23. C4×C131⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C131 | C22 | semidirect |
| 26. #127×C131 | C22 | semidirect |
| 31. C4×D4×C131 | C22 | semidirect |
| 71. D524 | #41 | semidirect |
| 88. C2×C4×C131 | D8 | semidirect |
| 120. C131 | #3100 | semidirect |
| 122. #532 | D131 | semidirect |
| 134. C4⋊Q8 | C2×D131 | semidirect |
| 135. #127 | C2×D131 | semidirect |
| 144. C4×D4 | C2×D131 | semidirect |
| 208. C2×C4 | #14523498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D524 | 2 |
| #22553623 | 2 |
| #22553589 | 2 |
| #22553504 | 2 |
| #22553445 | 2 |
| C4×#14523498 | 2 |
| #22553365 | 2 |
| #532×C131 | 2 |
| #3100 | 131 |