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×#16862274 | C2 | semidirect |
| 2. #22553862 | C2 | semidirect |
| 3. C2×C4×D524 | C2 | semidirect |
| 4. #22553528 | C2 | semidirect |
| 5. #22553518 | C2 | semidirect |
| 6. #22553508 | C2 | semidirect |
| 7. #22553314 | C2 | semidirect |
| 8. #423×C131 | C2 | semidirect |
| 15. #16862246 | C22 | semidirect |
| 16. #16862243 | C22 | semidirect |
| 17. #16862234 | C22 | semidirect |
| 28. #16862171 | C22 | semidirect |
| 29. #16862168 | C22 | semidirect |
| 32. C4⋊C8×C131 | C22 | semidirect |
| 33. C4⋊C8×C131 | C22 | semidirect |
| 42. C2×D524 | D4 | semidirect |
| 118. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 129. C131 | #3036 | semidirect |
| 137. #423 | D131 | semidirect |
| 160. C4⋊C8 | C2×D131 | semidirect |
| 161. C4⋊C8 | C2×D131 | semidirect |
| 250. C4 | #16862274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| #22553862 | 2 |
| C2×C4×D524 | 2 |
| #22553528 | 2 |
| #22553518 | 2 |
| #22553508 | 2 |
| #22553314 | 2 |
| #423×C131 | 2 |
| #3036 | 131 |