Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 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×#16862275 | C2 | semidirect |
| 2. C2×#16862270 | C2 | semidirect |
| 3. #22553860 | C2 | semidirect |
| 4. #124×D131 | C2 | semidirect |
| 5. #22553707 | C2 | semidirect |
| 6. #22553706 | C2 | semidirect |
| 7. #22553699 | C2 | semidirect |
| 8. #22553695 | C2 | semidirect |
| 9. #22553693 | C2 | semidirect |
| 10. #22553264 | C2 | semidirect |
| 11. #496×C131 | C2 | semidirect |
| 17. C2×Dic524 | C22 | semidirect |
| 18. C2×#14523503 | C22 | semidirect |
| 21. C2×#14523501 | C22 | semidirect |
| 24. #16862246 | C22 | semidirect |
| 28. #16862233 | C22 | semidirect |
| 34. #16862157 | C22 | semidirect |
| 35. C8×Dic131 | C22 | semidirect |
| 36. C2×SD16×C131 | C22 | semidirect |
| 38. #127×C131 | C22 | semidirect |
| 40. #97×C131 | C22 | semidirect |
| 62. #14523496 | D4 | semidirect |
| 134. C131 | #3153 | semidirect |
| 143. #496 | D131 | semidirect |
| 157. C2×SD16 | C2×D131 | semidirect |
| 162. #127 | C2×D131 | semidirect |
| 174. #97 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862275 | 2 |
| C2×#16862270 | 2 |
| #22553860 | 2 |
| #124×D131 | 2 |
| #22553707 | 2 |
| #22553706 | 2 |
| #22553699 | 2 |
| #22553695 | 2 |
| #22553693 | 2 |
| #22553264 | 2 |
| #496×C131 | 2 |
| #3153 | 131 |