Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#16862277 | C2 | semidirect |
| 3. #22553472 | C2 | semidirect |
| 4. #22553467 | C2 | semidirect |
| 5. #22553462 | C2 | semidirect |
| 6. #22553311 | C2 | semidirect |
| 7. #22553276 | C2 | semidirect |
| 8. C2×C22⋊Q8×C131 | C2 | semidirect |
| 19. C2×#14523503 | C22 | semidirect |
| 20. C2×#14523500 | C22 | semidirect |
| 21. C2×#14523497 | C22 | semidirect |
| 22. #16862169 | C22 | semidirect |
| 23. #16862166 | C22 | semidirect |
| 25. C22⋊(C131⋊C8) | C22 | semidirect |
| 26. C22×Q8×C131 | C22 | semidirect |
| 31. C22⋊Q8×C131 | C22 | semidirect |
| 33. C2×C4⋊C4×C131 | C22 | semidirect |
| 126. C22×C131 | #137 | semidirect |
| 146. C131 | #3007 | semidirect |
| 150. C2×C22⋊Q8 | D131 | semidirect |
| 162. C22×Q8 | C2×D131 | semidirect |
| 174. C22⋊Q8 | C2×D131 | semidirect |
| 176. C2×C4⋊C4 | C2×D131 | semidirect |
| 277. C22 | #16862277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523513 | 2 |
| C2×#16862277 | 2 |
| #22553472 | 2 |
| #22553467 | 2 |
| #22553462 | 2 |
| #22553311 | 2 |
| #22553276 | 2 |
| C2×C22⋊Q8×C131 | 2 |
| #3007 | 131 |