Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 2. #22553795 | C2 | semidirect |
| 3. #22553318 | C2 | semidirect |
| 4. #22553314 | C2 | semidirect |
| 5. #22553309 | C2 | semidirect |
| 6. C2×#16862168 | C2 | semidirect |
| 7. C2×#131×C131 | C2 | semidirect |
| 9. #16862292 | C4 | semidirect |
| 16. #16862205 | C22 | semidirect |
| 17. C2×C4⋊Dic131 | C22 | semidirect |
| 18. #16862171 | C22 | semidirect |
| 19. #16862171 | C22 | semidirect |
| 20. #16862168 | C22 | semidirect |
| 21. #16862168 | C22 | semidirect |
| 22. #16862168 | C22 | semidirect |
| 25. C2×M16×C131 | C22 | semidirect |
| 26. C22×C8×C131 | C22 | semidirect |
| 30. #14523513 | C2×C4 | semidirect |
| 34. C2×D524 | C2×C4 | semidirect |
| 97. C131 | #2897 | semidirect |
| 100. C2×#131 | D131 | semidirect |
| 114. C2×M16 | C2×D131 | semidirect |
| 115. C22×C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862292 | 2 |
| #22553795 | 2 |
| #22553318 | 2 |
| #22553314 | 2 |
| #22553309 | 2 |
| C2×#16862168 | 2 |
| C2×#131×C131 | 2 |
| #2897 | 131 |