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. C22×#14523500 | C2 | semidirect |
| 2. C2×#16862253 | C2 | semidirect |
| 4. #22553560 | C2 | semidirect |
| 5. #22553543 | C2 | semidirect |
| 6. #22553348 | C2 | semidirect |
| 7. #22553321 | C2 | semidirect |
| 8. #22553316 | C2 | semidirect |
| 9. #536×C131 | C2 | semidirect |
| 16. C2×#14523497 | C22 | semidirect |
| 18. C22×C131⋊C8 | C22 | semidirect |
| 24. #16862179 | C22 | semidirect |
| 25. #16862177 | C22 | semidirect |
| 26. #16862170 | C22 | semidirect |
| 33. C22⋊Q8×C131 | C22 | semidirect |
| 46. C2×C131⋊C8 | D4 | semidirect |
| 120. C131 | #3057 | semidirect |
| 124. #536 | D131 | semidirect |
| 147. C22⋊Q8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523500 | 2 |
| C2×#16862253 | 2 |
| #22553876 | 2 |
| #22553560 | 2 |
| #22553543 | 2 |
| #22553348 | 2 |
| #22553321 | 2 |
| #22553316 | 2 |
| #536×C131 | 2 |
| #3057 | 131 |