Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22553608 | C2 | semidirect |
| 5. #22553607 | C2 | semidirect |
| 6. #22553519 | C2 | semidirect |
| 8. Q16×Dic131 | C2 | semidirect |
| 9. #22553404 | C2 | semidirect |
| 11. #462×C131 | C2 | semidirect |
| 98. C4×D131 | Q16 | semidirect |
| 132. C131 | #3104 | semidirect |
| 140. #462 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553867 | 2 |
| C4×Q8×D131 | 2 |
| #22553646 | 2 |
| #22553608 | 2 |
| #22553607 | 2 |
| #22553519 | 2 |
| #22553466 | 2 |
| Q16×Dic131 | 2 |
| #22553404 | 2 |
| #22553364 | 2 |
| #462×C131 | 2 |
| #3104 | 131 |