Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 3. C4×#14523513 | C2 | semidirect |
| 4. #22553531 | C2 | semidirect |
| 5. #22553524 | C2 | semidirect |
| 6. #22553336 | C2 | semidirect |
| 7. #22553321 | C2 | semidirect |
| 8. #22553317 | C2 | semidirect |
| 9. C2×#124×C131 | C2 | semidirect |
| 13. C2×#14523503 | C22 | semidirect |
| 15. C2×#14523500 | C22 | semidirect |
| 19. C4×Dic262 | C22 | semidirect |
| 20. C4×D524 | C22 | semidirect |
| 25. C4⋊(C131⋊C8) | C22 | semidirect |
| 26. #16862170 | C22 | semidirect |
| 125. C131 | #3040 | semidirect |
| 129. C2×#124 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| C2×#16862272 | 2 |
| C4×#14523513 | 2 |
| #22553531 | 2 |
| #22553524 | 2 |
| #22553336 | 2 |
| #22553321 | 2 |
| #22553317 | 2 |
| C2×#124×C131 | 2 |
| #3040 | 131 |