Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#16861241 | C2 | semidirect |
| 3. C2×Q16×D127 | C2 | semidirect |
| 4. #22550451 | C2 | semidirect |
| 5. #22550269 | C2 | semidirect |
| 6. #22550268 | C2 | semidirect |
| 7. #22550261 | C2 | semidirect |
| 8. #22550260 | C2 | semidirect |
| 9. #22550254 | C2 | semidirect |
| 10. #22549830 | C2 | semidirect |
| 11. #494×C127 | C2 | semidirect |
| 122. C127 | #3156 | semidirect |
| 132. #494 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861241 | 2 |
| C2×#16861232 | 2 |
| C2×Q16×D127 | 2 |
| #22550451 | 2 |
| #22550269 | 2 |
| #22550268 | 2 |
| #22550261 | 2 |
| #22550260 | 2 |
| #22550254 | 2 |
| #22549830 | 2 |
| #494×C127 | 2 |
| #3156 | 127 |