Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 2. #22550219 | C2 | semidirect |
| 3. #22550213 | C2 | semidirect |
| 4. #22550180 | C2 | semidirect |
| 5. #22550135 | C2 | semidirect |
| 6. C4×Dic508 | C2 | semidirect |
| 8. #22549915 | C2 | semidirect |
| 9. #499×C127 | C2 | semidirect |
| 97. C127 | #3352 | semidirect |
| 99. #499 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550564 | 2 |
| #22550219 | 2 |
| #22550213 | 2 |
| #22550180 | 2 |
| #22550135 | 2 |
| C4×Dic508 | 2 |
| #22549955 | 2 |
| #22549915 | 2 |
| #499×C127 | 2 |
| #3352 | 127 |