Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22554019 | C2 | semidirect |
| 2. #22553658 | C2 | semidirect |
| 3. #22553628 | C2 | semidirect |
| 4. #22553602 | C2 | semidirect |
| 5. #22553539 | C2 | semidirect |
| 6. #22553509 | C2 | semidirect |
| 7. #22553463 | C2 | semidirect |
| 8. C4×#14523501 | C2 | semidirect |
| 9. D4×C131⋊C8 | C2 | semidirect |
| 10. C2×#16862167 | C2 | semidirect |
| 13. C2×#14523501 | C22 | semidirect |
| 14. C22×C131⋊C8 | C22 | semidirect |
| 15. #16862246 | C22 | semidirect |
| 17. #16862225 | C22 | semidirect |
| 19. C4×Dic262 | C22 | semidirect |
| 21. C2×C4⋊Dic131 | C22 | semidirect |
| 22. #16862177 | C22 | semidirect |
| 23. #16862177 | C22 | semidirect |
| 24. C4⋊(C131⋊C8) | C22 | semidirect |
| 25. #16862169 | C22 | semidirect |
| 28. #16862167 | C22 | semidirect |
| 29. #16862167 | C22 | semidirect |
| 30. #16862167 | C22 | semidirect |
| 31. C22⋊(C131⋊C8) | C22 | semidirect |
| 32. C4×C131⋊C8 | C22 | semidirect |
| 100. D4×C131 | SD16 | semidirect |
| 136. C131 | #3295 | semidirect |
| 230. D4 | #14523501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554019 | 2 |
| #22553658 | 2 |
| #22553628 | 2 |
| #22553602 | 2 |
| #22553539 | 2 |
| #22553509 | 2 |
| #22553463 | 2 |
| C4×#14523501 | 2 |
| D4×C131⋊C8 | 2 |
| C2×#16862167 | 2 |
| D42×C131 | 2 |
| #3295 | 131 |