Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
5872 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3213 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×#16862294 | C2 | semidirect |
| 2. C2×#16862293 | C2 | semidirect |
| 3. 2−1+4×D131 | C2 | direct (N × H) |
| 4. C2×#41×D131 | C2 | semidirect |
| 5. C22×Q8×D131 | C2 | semidirect |
| 6. C2×2−1+4×C131 | C2 | semidirect |
| 7. #16862294 | C22 | semidirect |
| 8. #16862293 | C22 | semidirect |
| 9. C2×#14523514 | C22 | semidirect |
| 10. C2×#14523513 | C22 | semidirect |
| 11. C2×#14523512 | C22 | semidirect |
| 12. #41×D131 | C22 | semidirect |
| 13. C22×Dic262 | C22 | semidirect |
| 15. C2×Q8×D131 | C22 | semidirect |
| 16. C2×Q8×D131 | C22 | semidirect |
| 19. 2−1+4×C131 | C22 | semidirect |
| 20. C2×#41×C131 | C22 | semidirect |
| 21. C22×Q8×C131 | C22 | semidirect |
| 23. #14523514 | C23 | semidirect |
| 24. #14523513 | C23 | semidirect |
| 25. #14523512 | C23 | semidirect |
| 27. C2×Dic262 | C23 | semidirect |
| 29. Q8×D131 | C23 | semidirect |
| 37. #41×C131 | C23 | semidirect |
| 39. C2×Q8×C131 | C23 | semidirect |
| 63. C2×D131 | 2−1+4 | direct (N × H) |
| 69. C2×C131 | C2×2−1+4 | semidirect |
| 72. D131 | C2×2−1+4 | direct (N × H) |
| 73. C131 | C22×2−1+4 | semidirect |
| 78. C2×2−1+4 | D131 | direct (N × H) |
| 83. 2−1+4 | C2×D131 | direct (N × H) |
| 88. C2×#41 | C2×D131 | semidirect |
| 93. C22×Q8 | C2×D131 | semidirect |
| 100. #41 | C22×D131 | semidirect |
| 106. C2×Q8 | C22×D131 | semidirect |
| 145. C2 | 2−1+4×D131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862294 | 2 |
| C2×#16862293 | 2 |
| 2−1+4×D131 | 2 |
| C2×#41×D131 | 2 |
| C22×Q8×D131 | 2 |
| C2×2−1+4×C131 | 2 |
| C22×2−1+4 | 131 |