Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
528 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 221 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. #22553787 | C2 | semidirect |
| 2. #22553424 | C2 | semidirect |
| 3. D8×Dic131 | C2 | semidirect |
| 4. #22553350 | C2 | semidirect |
| 5. #22553317 | C2 | semidirect |
| 6. #22553267 | C2 | semidirect |
| 10. D4×Dic131 | C22 | semidirect |
| 14. #16862180 | C22 | semidirect |
| 15. #16862178 | C22 | semidirect |
| 16. #16862167 | C22 | semidirect |
| 17. #16862156 | C22 | semidirect |
| 18. C8×Dic131 | C22 | semidirect |
| 20. C2×D8×C131 | C4 | semidirect |
| 37. C2×D4×C131 | C2×C4 | semidirect |
| 40. D8×C131 | C2×C4 | semidirect |
| 41. D8×C131 | C2×C4 | semidirect |
| 42. C2×C8×C131 | C2×C4 | semidirect |
| 77. C131 | #2948 | semidirect |
| 87. C2×D8 | Dic131 | semidirect |
| 105. C2×D4 | C2×Dic131 | semidirect |
| 109. D8 | C2×Dic131 | semidirect |
| 110. D8 | C2×Dic131 | semidirect |
| 113. C2×C8 | C2×Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553787 | 2 |
| #22553424 | 2 |
| D8×Dic131 | 2 |
| #22553350 | 2 |
| #22553317 | 2 |
| #22553267 | 2 |
| C22×D8×C131 | 2 |
| #2948 | 131 |