Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22550690 | C2 | semidirect |
| 2. #22550689 | C2 | semidirect |
| 3. #22550319 | C2 | semidirect |
| 4. #22550318 | C2 | semidirect |
| 5. #22550315 | C2 | semidirect |
| 6. #22550307 | C2 | semidirect |
| 7. #22550306 | C2 | semidirect |
| 8. C2×#16861155 | C2 | semidirect |
| 9. Q32×D127 | C2 | semidirect |
| 10. #22550294 | C2 | semidirect |
| 11. #510×C127 | C2 | semidirect |
| 124. C127 | #3417 | semidirect |
| 130. #510 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550690 | 2 |
| #22550689 | 2 |
| #22550319 | 2 |
| #22550318 | 2 |
| #22550315 | 2 |
| #22550307 | 2 |
| #22550306 | 2 |
| C2×#16861155 | 2 |
| Q32×D127 | 2 |
| #22550294 | 2 |
| #510×C127 | 2 |
| #3417 | 127 |