Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22553064 | C2 | semidirect |
| 5. #22553063 | C2 | semidirect |
| 6. #22553062 | C2 | semidirect |
| 7. #335×C131 | C2 | semidirect |
| 75. C131 | #1574 | semidirect |
| 81. #335 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553364 | 2 |
| #22553363 | 2 |
| #22553334 | 2 |
| #22553064 | 2 |
| #22553063 | 2 |
| #22553062 | 2 |
| #335×C131 | 2 |
| #1574 | 131 |