Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22553363 | C2 | semidirect |
| 3. #22553334 | C2 | semidirect |
| 4. Q8⋊(C131⋊C8) | C2 | semidirect |
| 5. #22553041 | C2 | semidirect |
| 6. #22553039 | C2 | semidirect |
| 7. Q8⋊C8×C131 | C2 | semidirect |
| 105. C131 | #1495 | semidirect |
| 111. Q8⋊C8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553849 | 2 |
| #22553363 | 2 |
| #22553334 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| #22553041 | 2 |
| #22553039 | 2 |
| Q8⋊C8×C131 | 2 |
| #1495 | 131 |