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×#16862279 | C2 | semidirect |
| 2. C2×#16862266 | C2 | semidirect |
| 3. C22×#14523501 | C2 | semidirect |
| 4. #22553883 | C2 | semidirect |
| 5. #22553879 | C2 | semidirect |
| 6. #22553703 | C2 | semidirect |
| 7. #22553700 | C2 | semidirect |
| 8. #22553695 | C2 | semidirect |
| 9. #22553683 | C2 | semidirect |
| 10. #22553270 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C131 | C2 | semidirect |
| 16. C2×Dic524 | C22 | semidirect |
| 17. C2×#14523503 | C22 | semidirect |
| 18. C2×#14523502 | C22 | semidirect |
| 22. C2×#14523501 | C22 | semidirect |
| 23. C2×#14523500 | C22 | semidirect |
| 24. C2×#14523498 | C22 | semidirect |
| 26. #16862244 | C22 | semidirect |
| 29. #16862233 | C22 | semidirect |
| 35. #16862156 | C22 | semidirect |
| 36. C8×Dic131 | C22 | semidirect |
| 63. C2×C131⋊C8 | D4 | semidirect |
| 86. M16×C131 | D4 | semidirect |
| 148. C131 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D131 | semidirect |
| 226. M16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862279 | 2 |
| C2×#16862266 | 2 |
| C22×#14523501 | 2 |
| #22553883 | 2 |
| #22553879 | 2 |
| #22553703 | 2 |
| #22553700 | 2 |
| #22553695 | 2 |
| #22553683 | 2 |
| #22553270 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| #3154 | 131 |