Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22550587 | C2 | semidirect |
| 3. #22550219 | C2 | semidirect |
| 4. #22550191 | C2 | semidirect |
| 5. #22550168 | C2 | semidirect |
| 6. #22550163 | C2 | semidirect |
| 7. #22550123 | C2 | semidirect |
| 8. C4×#14523237 | C2 | semidirect |
| 9. #22549955 | C2 | semidirect |
| 10. #22549917 | C2 | semidirect |
| 11. #500×C127 | C2 | semidirect |
| 122. C127 | #3357 | semidirect |
| 125. #500 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550592 | 2 |
| #22550587 | 2 |
| #22550219 | 2 |
| #22550191 | 2 |
| #22550168 | 2 |
| #22550163 | 2 |
| #22550123 | 2 |
| C4×#14523237 | 2 |
| #22549955 | 2 |
| #22549917 | 2 |
| #500×C127 | 2 |
| #3357 | 127 |