Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#14523500 | C2 | semidirect |
| 2. C2×#16862254 | C2 | semidirect |
| 3. #22553886 | C2 | semidirect |
| 5. #22553561 | C2 | semidirect |
| 6. #22553544 | C2 | semidirect |
| 7. #22553348 | C2 | semidirect |
| 8. #22553318 | C2 | semidirect |
| 9. #419×C131 | C2 | semidirect |
| 16. C2×#14523496 | C22 | semidirect |
| 18. C2×C8×D131 | C22 | semidirect |
| 24. #16862222 | C22 | semidirect |
| 28. #16862179 | C22 | semidirect |
| 29. #16862177 | C22 | semidirect |
| 34. #103×C131 | C22 | semidirect |
| 50. C2×C131⋊C8 | D4 | semidirect |
| 120. C131 | #3057 | semidirect |
| 129. #419 | D131 | semidirect |
| 154. #103 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523500 | 2 |
| C2×#16862254 | 2 |
| #22553886 | 2 |
| #22553881 | 2 |
| #22553561 | 2 |
| #22553544 | 2 |
| #22553348 | 2 |
| #22553318 | 2 |
| #419×C131 | 2 |
| #3057 | 131 |