Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. #22553179 | C2 | semidirect |
| 3. #22553176 | C2 | semidirect |
| 6. #22553163 | C2 | semidirect |
| 8. #22553157 | C2 | semidirect |
| 14. C2×C4×Dic131 | C4 | semidirect |
| 98. C131 | #2283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic131 | 2 |
| #22553179 | 2 |
| #22553176 | 2 |
| #22553175 | 2 |
| #22553170 | 2 |
| #22553163 | 2 |
| C22⋊C4×Dic131 | 2 |
| #22553157 | 2 |
| #381×C131 | 2 |
| #2283 | 131 |