Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #22553786 | C2 | semidirect |
| 3. #22553425 | C2 | semidirect |
| 4. C4×D1048 | C2 | semidirect |
| 5. #22553350 | C2 | semidirect |
| 6. #22553318 | C2 | semidirect |
| 7. #405×C131 | C2 | semidirect |
| 9. C2×D1048 | C4 | semidirect |
| 12. C4×D524 | C22 | semidirect |
| 16. #16862180 | C22 | semidirect |
| 17. #16862178 | C22 | semidirect |
| 18. #16862168 | C22 | semidirect |
| 22. #97×C131 | C22 | semidirect |
| 23. C4×C8×C131 | C22 | semidirect |
| 27. C2×D524 | C2×C4 | semidirect |
| 30. D1048 | C2×C4 | semidirect |
| 31. D1048 | C2×C4 | semidirect |
| 38. C2×C8×C131 | C2×C4 | semidirect |
| 77. C131 | #2948 | semidirect |
| 85. #405 | D131 | semidirect |
| 100. #97 | C2×D131 | semidirect |
| 101. C4×C8 | C2×D131 | semidirect |
| 112. C2×C8 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1048 | 2 |
| #22553786 | 2 |
| #22553425 | 2 |
| C4×D1048 | 2 |
| #22553350 | 2 |
| #22553318 | 2 |
| #405×C131 | 2 |
| #2948 | 131 |