Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#16862266 | C2 | semidirect |
| 2. C2×#16862254 | C2 | semidirect |
| 3. #22553893 | C2 | semidirect |
| 4. #22553890 | C2 | semidirect |
| 5. #22553569 | C2 | semidirect |
| 6. #22553564 | C2 | semidirect |
| 7. #22553544 | C2 | semidirect |
| 8. #22553540 | C2 | semidirect |
| 9. C2×#16862177 | C2 | semidirect |
| 10. #22553314 | C2 | semidirect |
| 11. #417×C131 | C2 | semidirect |
| 63. C2×C131⋊C8 | D4 | semidirect |
| 152. C131 | #3060 | semidirect |
| 164. #417 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862266 | 2 |
| C2×#16862254 | 2 |
| #22553893 | 2 |
| #22553890 | 2 |
| #22553569 | 2 |
| #22553564 | 2 |
| #22553544 | 2 |
| #22553540 | 2 |
| C2×#16862177 | 2 |
| #22553314 | 2 |
| #417×C131 | 2 |
| #3060 | 131 |