Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16862271 | C2 | semidirect |
| 2. C22×#14523498 | C2 | semidirect |
| 3. #22553876 | C2 | semidirect |
| 4. #22553457 | C2 | semidirect |
| 5. #22553446 | C2 | semidirect |
| 6. #22553317 | C2 | semidirect |
| 7. #22553308 | C2 | semidirect |
| 8. #22553279 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C131 | C2 | semidirect |
| 10. C22×D524 | C22 | semidirect |
| 12. C2×#14523500 | C22 | semidirect |
| 14. C2×#14523498 | C22 | semidirect |
| 15. C2×#14523498 | C22 | semidirect |
| 16. C2×#14523497 | C22 | semidirect |
| 17. C22×C131⋊C8 | C22 | semidirect |
| 20. #16862220 | C22 | semidirect |
| 22. #16862205 | C22 | semidirect |
| 23. #16862170 | C22 | semidirect |
| 24. #16862167 | C22 | semidirect |
| 25. #16862167 | C22 | semidirect |
| 26. C22⋊(C131⋊C8) | C22 | semidirect |
| 32. C2×#41×C131 | C22 | semidirect |
| 36. C22×D4×C131 | C22 | semidirect |
| 62. #41×C131 | D4 | semidirect |
| 76. C2×D4×C131 | D4 | semidirect |
| 151. C131 | #3008 | semidirect |
| 153. C2×H(5,𝔽2) | D131 | semidirect |
| 167. C2×#41 | C2×D131 | semidirect |
| 172. C22×D4 | C2×D131 | semidirect |
| 198. #41 | C22⋊D131 | semidirect |
| 217. C2×D4 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| C22×#14523498 | 2 |
| #22553876 | 2 |
| #22553457 | 2 |
| #22553446 | 2 |
| #22553317 | 2 |
| #22553308 | 2 |
| #22553279 | 2 |
| C2×H(5,𝔽2)×C131 | 2 |
| #3008 | 131 |