Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22550433 | C2 | semidirect |
| 3. #22550177 | C2 | semidirect |
| 4. #22550167 | C2 | semidirect |
| 5. #22550157 | C2 | semidirect |
| 6. #22549918 | C2 | semidirect |
| 8. #423×C127 | C2 | semidirect |
| 11. #16861209 | C22 | semidirect |
| 12. #16861209 | C22 | semidirect |
| 13. #16861201 | C22 | semidirect |
| 25. #16861143 | C22 | semidirect |
| 26. #16861141 | C22 | semidirect |
| 31. C4⋊C8×C127 | C22 | semidirect |
| 32. C4⋊C8×C127 | C22 | semidirect |
| 38. C2×D508 | Q8 | semidirect |
| 116. C127 | #3077 | semidirect |
| 123. #423 | D127 | semidirect |
| 145. C4⋊C8 | C2×D127 | semidirect |
| 146. C4⋊C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550433 | 2 |
| C2×C4×D508 | 2 |
| #22550177 | 2 |
| #22550167 | 2 |
| #22550157 | 2 |
| #22549918 | 2 |
| #22549882 | 2 |
| #423×C127 | 2 |
| #3077 | 127 |