Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
168 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #22553064 | C2 | semidirect |
| 4. #22553063 | C2 | semidirect |
| 5. #334×C131 | C2 | semidirect |
| 64. C131 | #1568 | semidirect |
| 70. #334 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553368 | 2 |
| C4×C8×D131 | 2 |
| #22553064 | 2 |
| #22553063 | 2 |
| #334×C131 | 2 |
| #1568 | 131 |