Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14523503 | C2 | semidirect |
| 3. #22553886 | C2 | semidirect |
| 4. #22553471 | C2 | semidirect |
| 5. #22553466 | C2 | semidirect |
| 6. #22553322 | C2 | semidirect |
| 7. #22553308 | C2 | semidirect |
| 8. #22553280 | C2 | semidirect |
| 9. C2×#137×C131 | C2 | semidirect |
| 140. C131 | #3011 | semidirect |
| 143. C2×#137 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862293 | 2 |
| C22×#14523503 | 2 |
| #22553886 | 2 |
| #22553471 | 2 |
| #22553466 | 2 |
| #22553322 | 2 |
| #22553308 | 2 |
| #22553280 | 2 |
| C2×#137×C131 | 2 |
| #3011 | 131 |