Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #22553270 | C2 | semidirect |
| 5. C2×#16862156 | C2 | semidirect |
| 6. #22553073 | C2 | semidirect |
| 7. #341×C131 | C2 | semidirect |
| 10. #16862254 | C4 | semidirect |
| 16. #16862172 | C4 | semidirect |
| 17. #16862171 | C4 | semidirect |
| 18. #16862168 | C4 | semidirect |
| 98. C131 | #1765 | semidirect |
| 105. #341 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862254 | 2 |
| C2×#16862172 | 2 |
| #22553309 | 2 |
| #22553270 | 2 |
| C2×#16862156 | 2 |
| #22553073 | 2 |
| #341×C131 | 2 |
| #1765 | 131 |