Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. #22553636 | C2 | direct (N × H) |
| 3. C2×#16862179 | C2 | semidirect |
| 4. C2×#16862177 | C2 | semidirect |
| 5. C2×#16862166 | C2 | semidirect |
| 6. C2×#16862166 | C2 | semidirect |
| 7. C2×C22⋊(C131⋊C8) | C2 | semidirect |
| 8. C2×#117×C131 | C2 | semidirect |
| 17. #16862179 | C22 | semidirect |
| 18. #16862177 | C22 | semidirect |
| 19. #16862166 | C22 | semidirect |
| 20. #16862166 | C22 | semidirect |
| 21. C22⋊(C131⋊C8) | C22 | semidirect |
| 24. #117×C131 | C22 | semidirect |
| 109. C2×C131 | #482 | semidirect |
| 114. C131 | C2×#482 | semidirect |
| 117. C2×#117 | D131 | semidirect |
| 132. #117 | C2×D131 | semidirect |
| 225. C2 | #22553636 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862220 | 2 |
| #22553636 | 2 |
| C2×#16862179 | 2 |
| C2×#16862177 | 2 |
| C2×#16862166 | 2 |
| C2×C22⋊(C131⋊C8) | 2 |
| C2×#117×C131 | 2 |
| C2×#482 | 131 |