Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#16862277 | C2 | semidirect |
| 2. C2×#16862271 | C2 | semidirect |
| 3. C2×#16862266 | C2 | semidirect |
| 4. C22×#14523500 | C2 | semidirect |
| 5. #22553881 | C2 | semidirect |
| 6. #22553704 | C2 | semidirect |
| 7. #22553702 | C2 | semidirect |
| 8. #22553694 | C2 | semidirect |
| 9. #22553686 | C2 | semidirect |
| 10. #22553268 | C2 | semidirect |
| 11. #536×C131 | C2 | semidirect |
| 17. C2×#14523503 | C22 | semidirect |
| 18. C2×#14523503 | C22 | semidirect |
| 19. C2×#14523501 | C22 | semidirect |
| 24. C2×#14523500 | C22 | semidirect |
| 25. C2×#14523500 | C22 | semidirect |
| 27. C2×#14523498 | C22 | semidirect |
| 34. #16862157 | C22 | semidirect |
| 35. C4×C131⋊C8 | C22 | semidirect |
| 38. C4⋊Q8×C131 | C22 | semidirect |
| 39. #124×C131 | C22 | semidirect |
| 65. #14523497 | D4 | semidirect |
| 66. C2×C131⋊C8 | D4 | semidirect |
| 148. C131 | #3154 | semidirect |
| 154. #536 | D131 | semidirect |
| 181. C4⋊Q8 | C2×D131 | semidirect |
| 184. #124 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| C2×#16862271 | 2 |
| C2×#16862266 | 2 |
| C22×#14523500 | 2 |
| #22553881 | 2 |
| #22553704 | 2 |
| #22553702 | 2 |
| #22553694 | 2 |
| #22553686 | 2 |
| #22553268 | 2 |
| #536×C131 | 2 |
| #3154 | 131 |