Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 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×#16862274 | C2 | semidirect |
| 2. #22553862 | C2 | semidirect |
| 3. C2×#16862243 | C2 | semidirect |
| 4. #22553701 | C2 | semidirect |
| 5. #22553689 | C2 | semidirect |
| 6. #22553685 | C2 | semidirect |
| 7. C4×M16×C131 | C2 | semidirect |
| 12. C2×#14523502 | C22 | semidirect |
| 13. C2×D1048 | C22 | semidirect |
| 14. #16862246 | C22 | semidirect |
| 18. #16862243 | C22 | semidirect |
| 19. #16862234 | C22 | semidirect |
| 24. #97×C131 | C22 | semidirect |
| 25. C4×C8×C131 | C22 | semidirect |
| 45. M16×C131 | D4 | semidirect |
| 71. C8×C131 | C2×D4 | semidirect |
| 82. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 90. C131 | #3151 | semidirect |
| 98. C4×M16 | D131 | semidirect |
| 115. #97 | C2×D131 | semidirect |
| 116. C4×C8 | C2×D131 | semidirect |
| 134. M16 | D524 | semidirect |
| 162. C8 | C2×D524 | semidirect |
| 174. C4 | #16862274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| #22553862 | 2 |
| C2×#16862243 | 2 |
| #22553701 | 2 |
| #22553689 | 2 |
| #22553685 | 2 |
| C4×M16×C131 | 2 |
| #3151 | 131 |