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×#16862279 | C2 | semidirect |
| 3. C2×#16862234 | C2 | semidirect |
| 4. C4×#14523513 | C2 | semidirect |
| 5. #22553535 | C2 | semidirect |
| 6. #22553528 | C2 | semidirect |
| 7. #22553322 | C2 | semidirect |
| 8. #22553318 | C2 | semidirect |
| 9. #423×C131 | C2 | semidirect |
| 15. C2×Dic524 | C22 | semidirect |
| 17. C2×#14523502 | C22 | semidirect |
| 22. C4×Dic262 | C22 | semidirect |
| 23. C4×D524 | C22 | semidirect |
| 29. #16862171 | C22 | semidirect |
| 34. C4⋊C8×C131 | C22 | semidirect |
| 125. C131 | #3040 | semidirect |
| 133. #423 | D131 | semidirect |
| 158. C4⋊C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862279 | 2 |
| C2×#16862274 | 2 |
| C2×#16862234 | 2 |
| C4×#14523513 | 2 |
| #22553535 | 2 |
| #22553528 | 2 |
| #22553322 | 2 |
| #22553318 | 2 |
| #423×C131 | 2 |
| #3040 | 131 |