Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#14523237 | C2 | semidirect |
| 3. #22550452 | C2 | semidirect |
| 4. #22550350 | C2 | semidirect |
| 5. #22550092 | C2 | semidirect |
| 6. #22550082 | C2 | semidirect |
| 7. #22549886 | C2 | semidirect |
| 8. #22549873 | C2 | semidirect |
| 9. #424×C127 | C2 | semidirect |
| 18. #16861209 | C22 | semidirect |
| 19. #16861197 | C22 | semidirect |
| 26. #16861134 | C22 | semidirect |
| 27. #16861134 | C22 | semidirect |
| 28. #16861131 | C22 | semidirect |
| 32. C4⋊C8×C127 | C22 | semidirect |
| 117. C127 | #3042 | semidirect |
| 124. #424 | 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 |
|---|---|
| C2×#16861237 | 2 |
| C22×#14523237 | 2 |
| #22550452 | 2 |
| #22550350 | 2 |
| #22550092 | 2 |
| #22550082 | 2 |
| #22549886 | 2 |
| #22549873 | 2 |
| #424×C127 | 2 |
| #3042 | 127 |