Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#16862271 | C2 | semidirect |
| 2. C2×C4×D524 | C2 | semidirect |
| 3. #22553524 | C2 | semidirect |
| 4. #22553514 | C2 | semidirect |
| 5. #22553504 | C2 | semidirect |
| 6. #22553336 | C2 | semidirect |
| 7. #22553313 | C2 | semidirect |
| 8. #532×C131 | C2 | semidirect |
| 21. C4⋊(C131⋊C8) | C22 | semidirect |
| 22. C4⋊(C131⋊C8) | C22 | semidirect |
| 23. #16862170 | C22 | semidirect |
| 24. #16862167 | C22 | semidirect |
| 26. C4⋊Q8×C131 | C22 | semidirect |
| 27. #127×C131 | C22 | semidirect |
| 28. #124×C131 | C22 | semidirect |
| 37. C2×D524 | D4 | semidirect |
| 119. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 129. C131 | #3036 | semidirect |
| 132. #532 | D131 | semidirect |
| 146. C4⋊Q8 | C2×D131 | semidirect |
| 147. #127 | C2×D131 | semidirect |
| 148. #124 | C2×D131 | semidirect |
| 250. C4 | #16862271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| C2×C4×D524 | 2 |
| #22553524 | 2 |
| #22553514 | 2 |
| #22553504 | 2 |
| #22553336 | 2 |
| #22553313 | 2 |
| #532×C131 | 2 |
| #3036 | 131 |