Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 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. #22550354 | C2 | semidirect |
| 4. #22549979 | C2 | semidirect |
| 5. #22549961 | C2 | semidirect |
| 6. #22549912 | C2 | semidirect |
| 8. #22549834 | C2 | semidirect |
| 9. #419×C127 | C2 | semidirect |
| 11. C2×#14523235 | C4 | semidirect |
| 16. Q8×Dic127 | C22 | semidirect |
| 23. #16861142 | C22 | semidirect |
| 24. #16861140 | C22 | semidirect |
| 26. #16861119 | C22 | semidirect |
| 27. C8×Dic127 | C22 | semidirect |
| 31. #103×C127 | C22 | semidirect |
| 38. #14523235 | C2×C4 | semidirect |
| 39. #14523235 | C2×C4 | semidirect |
| 40. C2×C127⋊C8 | C2×C4 | semidirect |
| 54. C2×Q8×C127 | C2×C4 | semidirect |
| 104. C127 | #2949 | semidirect |
| 111. #419 | D127 | semidirect |
| 132. #103 | C2×D127 | semidirect |
| 139. C2×Q8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523235 | 2 |
| #22550354 | 2 |
| #22550350 | 2 |
| #22549979 | 2 |
| #22549961 | 2 |
| #22549912 | 2 |
| #22549882 | 2 |
| #22549834 | 2 |
| #419×C127 | 2 |
| #2949 | 127 |