Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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. #22553871 | C2 | semidirect |
| 2. #22553502 | C2 | semidirect |
| 3. #22553499 | C2 | semidirect |
| 4. C2×#16862161 | C2 | semidirect |
| 5. C2×H(5,𝔽2)×C131 | C2 | semidirect |
| 6. C22×C22⋊D131 | C22 | semidirect |
| 8. #16862227 | C22 | semidirect |
| 11. #16862214 | C22 | semidirect |
| 12. C2×C22⋊Dic131 | C22 | semidirect |
| 13. #16862161 | C22 | semidirect |
| 19. C23×D131 | C23 | semidirect |
| 24. C22×Dic131 | C23 | semidirect |
| 28. C22⋊Dic131 | C23 | semidirect |
| 31. C24×C131 | D4 | semidirect |
| 41. C2×D4×C131 | D4 | semidirect |
| 44. C22×C4×C131 | D4 | semidirect |
| 93. C131 | #3026 | semidirect |
| 95. C2×H(5,𝔽2) | D131 | semidirect |
| 115. C24 | C22⋊D131 | semidirect |
| 128. C2×D4 | C22⋊D131 | semidirect |
| 133. C22×C4 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553871 | 2 |
| #22553502 | 2 |
| #22553499 | 2 |
| C2×#16862161 | 2 |
| C2×H(5,𝔽2)×C131 | 2 |
| #3026 | 131 |