Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862272 | C2 | semidirect |
| 2. C4×#14523513 | C2 | semidirect |
| 3. #22553509 | C2 | semidirect |
| 4. #22553504 | C2 | semidirect |
| 5. #22553336 | C2 | semidirect |
| 6. #22553317 | C2 | semidirect |
| 7. C2×#127×C131 | C2 | semidirect |
| 10. C2×#14523501 | C22 | semidirect |
| 11. C2×#14523498 | C22 | semidirect |
| 13. C4×Dic262 | C22 | semidirect |
| 14. C4×D524 | C22 | semidirect |
| 19. C4⋊(C131⋊C8) | C22 | semidirect |
| 20. #16862167 | C22 | semidirect |
| 28. #14523513 | D4 | semidirect |
| 59. Dic262 | C2×D4 | semidirect |
| 61. D524 | C2×D4 | semidirect |
| 94. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 104. C131 | #3038 | semidirect |
| 107. C2×#127 | D131 | semidirect |
| 201. C4 | #16862272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862272 | 2 |
| C4×#14523513 | 2 |
| #22553509 | 2 |
| #22553504 | 2 |
| #22553336 | 2 |
| #22553317 | 2 |
| C2×#127×C131 | 2 |
| #3038 | 131 |