Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#16862270 | C2 | semidirect |
| 2. #22553860 | C2 | semidirect |
| 3. #127×D131 | C2 | semidirect |
| 4. #22553700 | C2 | semidirect |
| 5. #22553688 | C2 | semidirect |
| 6. #22553685 | C2 | semidirect |
| 7. #22553684 | C2 | semidirect |
| 8. C4×#14523496 | C2 | semidirect |
| 9. #493×C131 | C2 | semidirect |
| 14. C2×#14523502 | C22 | semidirect |
| 15. C2×#14523501 | C22 | semidirect |
| 16. C2×#14523498 | C22 | semidirect |
| 18. #16862246 | C22 | semidirect |
| 22. #16862233 | C22 | semidirect |
| 26. #16862156 | C22 | semidirect |
| 27. C4×C131⋊C8 | C22 | semidirect |
| 28. C2×D8×C131 | C22 | semidirect |
| 30. #127×C131 | C22 | semidirect |
| 31. C4×C8×C131 | C22 | semidirect |
| 48. #14523496 | D4 | semidirect |
| 77. C131⋊C8 | C2×D4 | semidirect |
| 86. C8×C131 | C2×D4 | semidirect |
| 97. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 108. C131 | #3151 | semidirect |
| 115. #493 | D131 | semidirect |
| 126. C2×D8 | C2×D131 | semidirect |
| 133. #127 | C2×D131 | semidirect |
| 140. C4×C8 | C2×D131 | semidirect |
| 195. C8 | D4×D131 | semidirect |
| 209. C4 | #16862270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862270 | 2 |
| #22553860 | 2 |
| #127×D131 | 2 |
| #22553700 | 2 |
| #22553688 | 2 |
| #22553685 | 2 |
| #22553684 | 2 |
| C4×#14523496 | 2 |
| #493×C131 | 2 |
| #3151 | 131 |