Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
256 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#16862181 | C2 | semidirect |
| 3. #22553348 | C2 | semidirect |
| 5. #22553083 | C2 | semidirect |
| 6. #22553082 | C2 | semidirect |
| 10. #16862253 | C4 | semidirect |
| 11. #16862253 | C4 | semidirect |
| 105. C131 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862253 | 2 |
| C2×#16862181 | 2 |
| #22553348 | 2 |
| #22553329 | 2 |
| #22553083 | 2 |
| #22553082 | 2 |
| #421×C131 | 2 |
| #1814 | 131 |