Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #22553715 | C2 | semidirect |
| 4. #22553059 | C2 | semidirect |
| 5. Q8⋊(C131⋊C8) | C2 | semidirect |
| 7. #462×C131 | C2 | semidirect |
| 55. D524 | Q16 | semidirect |
| 92. C131 | #1649 | semidirect |
| 97. #462 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D524 | 2 |
| #22553715 | 2 |
| #22553589 | 2 |
| #22553059 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| #22553039 | 2 |
| #462×C131 | 2 |
| #1649 | 131 |