Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×#16862211 | C2 | semidirect |
| 4. #22553217 | C2 | semidirect |
| 6. #22553202 | C2 | semidirect |
| 7. #22553183 | C2 | semidirect |
| 8. #22553158 | C2 | semidirect |
| 9. #384×C131 | C2 | semidirect |
| 13. #16862234 | C4 | semidirect |
| 33. C2×Dic262 | C2×C4 | semidirect |
| 46. (C2×D131)⋊C4 | C2×C4 | semidirect |
| 57. C42×C131 | C2×C4 | semidirect |
| 111. C131 | #2326 | semidirect |
| 120. #384 | D131 | semidirect |
| 169. C42 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862234 | 2 |
| C2×#16862211 | 2 |
| C2×#16862208 | 2 |
| #22553217 | 2 |
| #22553213 | 2 |
| #22553202 | 2 |
| #22553183 | 2 |
| #22553158 | 2 |
| #384×C131 | 2 |
| #2326 | 131 |