Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22550601 | C2 | semidirect |
| 3. #22550229 | C2 | semidirect |
| 4. #22550174 | C2 | semidirect |
| 5. #22550158 | C2 | semidirect |
| 6. #22550097 | C2 | semidirect |
| 8. C8×Dic254 | C2 | semidirect |
| 9. C4×Dic508 | C2 | semidirect |
| 10. #22549967 | C2 | semidirect |
| 118. C127 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550612 | 2 |
| #22550601 | 2 |
| #22550229 | 2 |
| #22550174 | 2 |
| #22550158 | 2 |
| #22550097 | 2 |
| #22550073 | 2 |
| C8×Dic254 | 2 |
| C4×Dic508 | 2 |
| #22549967 | 2 |
| #486×C127 | 2 |
| #3365 | 127 |