Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16862205 | C2 | semidirect |
| 2. #22553633 | C2 | semidirect |
| 3. #22553628 | C2 | semidirect |
| 4. #22553623 | C2 | semidirect |
| 5. #22553352 | C2 | semidirect |
| 6. #22553317 | C2 | semidirect |
| 7. #22553276 | C2 | semidirect |
| 13. #16862205 | C22 | semidirect |
| 14. C2×C4⋊Dic131 | C22 | semidirect |
| 15. C2×C4⋊Dic131 | C22 | semidirect |
| 18. #16862179 | C22 | semidirect |
| 19. #16862177 | C22 | semidirect |
| 20. #16862167 | C22 | semidirect |
| 21. #16862167 | C22 | semidirect |
| 22. C22⋊(C131⋊C8) | C22 | semidirect |
| 23. C22⋊(C131⋊C8) | C22 | semidirect |
| 125. C131 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862205 | 2 |
| #22553633 | 2 |
| #22553628 | 2 |
| #22553623 | 2 |
| #22553352 | 2 |
| #22553317 | 2 |
| #22553276 | 2 |
| C2×#121×C131 | 2 |
| #3094 | 131 |