Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 1. C2×#16862277 | C2 | semidirect |
| 2. C22×#14523500 | C2 | semidirect |
| 4. #22553534 | C2 | semidirect |
| 5. #22553512 | C2 | semidirect |
| 6. #22553339 | C2 | semidirect |
| 7. #22553316 | C2 | semidirect |
| 8. #22553306 | C2 | semidirect |
| 9. #519×C131 | C2 | semidirect |
| 13. C2×#14523503 | C22 | semidirect |
| 16. C2×#14523500 | C22 | semidirect |
| 23. C4⋊(C131⋊C8) | C22 | semidirect |
| 24. #16862169 | C22 | semidirect |
| 26. #16862166 | C22 | semidirect |
| 29. C4×Q8×C131 | C22 | semidirect |
| 55. C2×Q8×C131 | D4 | semidirect |
| 116. C131 | #3043 | semidirect |
| 121. #519 | D131 | semidirect |
| 142. C4×Q8 | C2×D131 | semidirect |
| 156. C2×Q8 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| C22×#14523500 | 2 |
| #22553881 | 2 |
| #22553534 | 2 |
| #22553512 | 2 |
| #22553339 | 2 |
| #22553316 | 2 |
| #22553306 | 2 |
| #519×C131 | 2 |
| #3043 | 131 |