Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
152 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 40. C8×C131 | Q16 | semidirect |
| 52. C131 | #1591 | semidirect |
| 93. C8 | Dic524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553442 | 2 |
| C4×Dic524 | 2 |
| #22553065 | 2 |
| #22553044 | 2 |
| C82×C131 | 2 |
| #1591 | 131 |