Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #22550351 | C2 | semidirect |
| 3. #22550350 | C2 | semidirect |
| 4. #22549985 | C2 | semidirect |
| 5. #22549956 | C2 | semidirect |
| 6. #22549912 | C2 | semidirect |
| 7. #22549882 | C2 | semidirect |
| 8. #22549834 | C2 | semidirect |
| 9. #418×C127 | C2 | semidirect |
| 11. C2×#14523233 | C4 | semidirect |
| 17. D4×Dic127 | C22 | semidirect |
| 18. #16861171 | C22 | semidirect |
| 23. #16861142 | C22 | semidirect |
| 24. #16861140 | C22 | semidirect |
| 25. #16861131 | C22 | semidirect |
| 26. #16861119 | C22 | semidirect |
| 27. C8×Dic127 | C22 | semidirect |
| 31. #102×C127 | C22 | semidirect |
| 35. C2×D508 | C2×C4 | semidirect |
| 39. #14523233 | C2×C4 | semidirect |
| 40. #14523233 | C2×C4 | semidirect |
| 41. C2×C127⋊C8 | C2×C4 | semidirect |
| 55. C2×D4×C127 | C2×C4 | semidirect |
| 109. C127 | #2948 | semidirect |
| 117. #418 | D127 | semidirect |
| 138. #102 | C2×D127 | semidirect |
| 149. C2×D4 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523233 | 2 |
| #22550351 | 2 |
| #22550350 | 2 |
| #22549985 | 2 |
| #22549956 | 2 |
| #22549912 | 2 |
| #22549882 | 2 |
| #22549834 | 2 |
| #418×C127 | 2 |
| #2948 | 127 |