Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
296 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 9. C4×C131⋊C8 | C4 | semidirect |
| 12. C4×C8×C131 | C4 | semidirect |
| 18. C4×Dic131 | C8 | semidirect |
| 52. C131 | #1744 | semidirect |
| 65. C4×C8 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C131⋊C8 | 2 |
| C42×Dic131 | 2 |
| #22553066 | 2 |
| C2×C4×C8×C131 | 2 |
| #1744 | 131 |