Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #22550220 | C2 | semidirect |
| 4. #22550208 | C2 | semidirect |
| 5. #22550168 | C2 | semidirect |
| 6. #22550158 | C2 | semidirect |
| 7. #22550135 | C2 | semidirect |
| 8. C4×Dic508 | C2 | semidirect |
| 10. #22549915 | C2 | semidirect |
| 11. #498×C127 | C2 | semidirect |
| 117. C127 | #3356 | semidirect |
| 120. #498 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550600 | 2 |
| #22550587 | 2 |
| #22550220 | 2 |
| #22550208 | 2 |
| #22550168 | 2 |
| #22550158 | 2 |
| #22550135 | 2 |
| C4×Dic508 | 2 |
| #22549955 | 2 |
| #22549915 | 2 |
| #498×C127 | 2 |
| #3356 | 127 |