Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. #22553966 | C2 | semidirect |
| 2. #22553658 | C2 | semidirect |
| 3. #22553623 | C2 | semidirect |
| 4. #22553592 | C2 | semidirect |
| 5. #22553546 | C2 | semidirect |
| 6. #22553504 | C2 | semidirect |
| 7. #22553446 | C2 | semidirect |
| 8. C4×#14523498 | C2 | semidirect |
| 9. D4×C131⋊C8 | C2 | semidirect |
| 10. C2×#16862167 | C2 | semidirect |
| 11. D42×C131 | C2 | semidirect |
| 14. C2×#14523498 | C22 | semidirect |
| 15. C22×C131⋊C8 | C22 | semidirect |
| 16. #16862246 | C22 | semidirect |
| 19. #16862220 | C22 | semidirect |
| 20. C4×D524 | C22 | semidirect |
| 21. C2×C4⋊Dic131 | C22 | semidirect |
| 22. #16862179 | C22 | semidirect |
| 23. #16862179 | C22 | semidirect |
| 24. C4⋊(C131⋊C8) | C22 | semidirect |
| 27. #16862167 | C22 | semidirect |
| 28. #16862167 | C22 | semidirect |
| 29. #16862167 | C22 | semidirect |
| 30. #16862166 | C22 | semidirect |
| 31. C22⋊(C131⋊C8) | C22 | semidirect |
| 32. C4×C131⋊C8 | C22 | semidirect |
| 103. D4×C131 | D8 | semidirect |
| 104. D4×C131 | #41 | semidirect |
| 142. C131 | #3294 | semidirect |
| 145. D42 | D131 | semidirect |
| 239. D4 | #14523498 | semidirect |
| 240. D4 | #14523512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553966 | 2 |
| #22553658 | 2 |
| #22553623 | 2 |
| #22553592 | 2 |
| #22553546 | 2 |
| #22553504 | 2 |
| #22553446 | 2 |
| C4×#14523498 | 2 |
| D4×C131⋊C8 | 2 |
| C2×#16862167 | 2 |
| D42×C131 | 2 |
| #3294 | 131 |