Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C22×Dic524 | C2 | semidirect |
| 4. C2×#16862211 | C2 | semidirect |
| 5. #22553533 | C2 | direct (N × H) |
| 6. C2×Dic131⋊C8 | C2 | semidirect |
| 7. C2×#16862169 | C2 | semidirect |
| 12. C2×Dic524 | C22 | semidirect |
| 19. #16862211 | C22 | semidirect |
| 25. Dic131⋊C8 | C22 | semidirect |
| 26. #16862169 | C22 | semidirect |
| 111. C2×C131 | #464 | semidirect |
| 115. C131 | C2×#464 | semidirect |
| 227. C2 | #22553533 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic524 | 2 |
| C22×#14523501 | 2 |
| C2×#16862233 | 2 |
| C2×#16862211 | 2 |
| #22553533 | 2 |
| C2×Dic131⋊C8 | 2 |
| C2×#16862169 | 2 |
| C2×#102×C131 | 2 |
| C2×#464 | 131 |