Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. #22553862 | C2 | semidirect |
| 3. #22553699 | C2 | semidirect |
| 4. #22553688 | C2 | semidirect |
| 5. #22553684 | C2 | semidirect |
| 6. C4×#14523497 | C2 | semidirect |
| 7. C2×#127×C131 | C2 | semidirect |
| 10. C2×#14523501 | C22 | semidirect |
| 11. C2×#14523498 | C22 | semidirect |
| 13. #16862246 | C22 | semidirect |
| 14. #16862243 | C22 | semidirect |
| 15. #16862234 | C22 | semidirect |
| 18. #16862157 | C22 | semidirect |
| 19. C4×C131⋊C8 | C22 | semidirect |
| 34. #14523497 | D4 | semidirect |
| 57. C131⋊C8 | C2×D4 | semidirect |
| 82. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 90. C131 | #3151 | semidirect |
| 94. C2×#127 | D131 | semidirect |
| 174. 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 |
| #22553862 | 2 |
| #22553699 | 2 |
| #22553688 | 2 |
| #22553684 | 2 |
| C4×#14523497 | 2 |
| C2×#127×C131 | 2 |
| #3151 | 131 |