Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
460 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 20. C4⋊Q8×C131 | C4 | semidirect |
| 31. C4×Dic131 | Q8 | semidirect |
| 79. C131 | #2331 | semidirect |
| 89. C4⋊Q8 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553219 | 2 |
| #22553211 | 2 |
| #22553198 | 2 |
| #22553178 | 2 |
| C4⋊C4×Dic131 | 2 |
| #22553158 | 2 |
| C2×C4⋊Q8×C131 | 2 |
| #2331 | 131 |