Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862266 | C2 | semidirect |
| 2. #22553879 | C2 | semidirect |
| 3. #22553795 | C2 | semidirect |
| 4. #22553532 | C2 | semidirect |
| 5. #22553525 | C2 | semidirect |
| 6. #22553510 | C2 | semidirect |
| 7. #22553505 | C2 | semidirect |
| 8. #22553340 | C2 | semidirect |
| 9. #22553314 | C2 | semidirect |
| 10. C2×#16862167 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C131 | C2 | semidirect |
| 14. C2×#14523503 | C22 | semidirect |
| 15. C2×#14523501 | C22 | semidirect |
| 16. C2×#14523500 | C22 | semidirect |
| 17. C2×#14523498 | C22 | semidirect |
| 24. Q8×Dic131 | C22 | semidirect |
| 26. D4×Dic131 | C22 | semidirect |
| 31. Dic131⋊C8 | C22 | semidirect |
| 32. Dic131⋊C8 | C22 | semidirect |
| 33. #16862171 | C22 | semidirect |
| 34. #16862168 | C22 | semidirect |
| 73. #41×C131 | D4 | semidirect |
| 154. C131 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D131 | semidirect |
| 202. #41 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862266 | 2 |
| #22553879 | 2 |
| #22553795 | 2 |
| #22553532 | 2 |
| #22553525 | 2 |
| #22553510 | 2 |
| #22553505 | 2 |
| #22553340 | 2 |
| #22553314 | 2 |
| C2×#16862167 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| #3045 | 131 |