Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22550424 | C2 | semidirect |
| 2. C4×#14523249 | C2 | semidirect |
| 3. #22550198 | C2 | semidirect |
| 4. #22550161 | C2 | semidirect |
| 5. #22550157 | C2 | semidirect |
| 6. #22550068 | C2 | semidirect |
| 7. #22550020 | C2 | semidirect |
| 8. #22549985 | C2 | semidirect |
| 9. #22549977 | C2 | semidirect |
| 10. #22549932 | C2 | semidirect |
| 11. #460×C127 | C2 | semidirect |
| 88. D508 | #41 | semidirect |
| 106. Q8×C127 | #41 | semidirect |
| 145. C127 | #3115 | semidirect |
| 151. #460 | D127 | semidirect |
| 233. Q8 | #14523247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550424 | 2 |
| C4×#14523249 | 2 |
| #22550198 | 2 |
| #22550161 | 2 |
| #22550157 | 2 |
| #22550068 | 2 |
| #22550020 | 2 |
| #22549985 | 2 |
| #22549977 | 2 |
| #22549932 | 2 |
| #460×C127 | 2 |
| #3115 | 127 |