Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22550504 | C2 | semidirect |
| 3. #22550177 | C2 | semidirect |
| 4. #22550177 | C2 | semidirect |
| 5. #22550167 | C2 | semidirect |
| 6. #22550157 | C2 | semidirect |
| 7. #22549918 | C2 | semidirect |
| 8. #22549914 | C2 | semidirect |
| 11. #424×C127 | C2 | semidirect |
| 13. #16861209 | C22 | semidirect |
| 15. #16861201 | C22 | semidirect |
| 26. #16861143 | C22 | semidirect |
| 27. #16861143 | C22 | semidirect |
| 28. #16861143 | C22 | semidirect |
| 29. #16861141 | C22 | semidirect |
| 30. #16861141 | C22 | semidirect |
| 31. #16861141 | C22 | semidirect |
| 39. C4⋊C8×C127 | C22 | semidirect |
| 40. C4⋊C8×C127 | C22 | semidirect |
| 45. C2×D508 | Q8 | semidirect |
| 125. C127 | #3081 | semidirect |
| 134. #424 | D127 | semidirect |
| 160. C4⋊C8 | C2×D127 | semidirect |
| 161. C4⋊C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550504 | 2 |
| #22550350 | 2 |
| #22550177 | 2 |
| #22550167 | 2 |
| #22550157 | 2 |
| #22549918 | 2 |
| #22549914 | 2 |
| #22549882 | 2 |
| C2×#16861131 | 2 |
| #424×C127 | 2 |
| #3081 | 127 |