Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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. #22553609 | C2 | direct (N × H) |
| 3. C2×#16862179 | C2 | semidirect |
| 4. C2×#16862177 | C2 | semidirect |
| 5. C2×C4⋊(C131⋊C8) | C2 | semidirect |
| 8. C2×#125×C131 | C2 | semidirect |
| 17. #16862179 | C22 | semidirect |
| 18. #16862177 | C22 | semidirect |
| 19. C4⋊(C131⋊C8) | C22 | semidirect |
| 23. #125×C131 | C22 | semidirect |
| 98. C2×C131 | #478 | semidirect |
| 103. C131 | C2×#478 | semidirect |
| 105. C2×#125 | D131 | semidirect |
| 118. #125 | C2×D131 | semidirect |
| 203. C2 | #22553609 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D524 | 2 |
| #22553609 | 2 |
| C2×#16862179 | 2 |
| C2×#16862177 | 2 |
| C2×C4⋊(C131⋊C8) | 2 |
| C2×#16862166 | 2 |
| C2×#125×C131 | 2 |
| C2×#478 | 131 |