Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22553599 | C2 | direct (N × H) |
| 3. C2×#16862177 | C2 | semidirect |
| 4. C2×C4⋊(C131⋊C8) | C2 | semidirect |
| 6. C2×C4⋊Q8×C131 | C2 | semidirect |
| 14. #16862177 | C22 | semidirect |
| 15. C4⋊(C131⋊C8) | C22 | semidirect |
| 19. C4⋊Q8×C131 | C22 | semidirect |
| 26. C2×D524 | Q8 | semidirect |
| 53. D524 | C2×Q8 | semidirect |
| 85. C2×C131 | #476 | semidirect |
| 90. C131 | C2×#476 | semidirect |
| 92. C2×C4⋊Q8 | D131 | semidirect |
| 103. C4⋊Q8 | C2×D131 | semidirect |
| 177. C2 | #22553599 | 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 |
| #22553599 | 2 |
| C2×#16862177 | 2 |
| C2×C4⋊(C131⋊C8) | 2 |
| C2×#16862166 | 2 |
| C2×C4⋊Q8×C131 | 2 |
| C2×#476 | 131 |