Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
180 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22553065 | C2 | semidirect |
| 4. #22553062 | C2 | semidirect |
| 5. #335×C131 | C2 | semidirect |
| 24. C8×D131 | C8 | semidirect |
| 66. C131 | #1564 | semidirect |
| 71. #335 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553364 | 2 |
| C4×C8×D131 | 2 |
| #22553065 | 2 |
| #22553062 | 2 |
| #335×C131 | 2 |
| #1564 | 131 |