Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. #22550430 | C2 | semidirect |
| 3. #22550168 | C2 | semidirect |
| 4. #22550155 | C2 | semidirect |
| 5. #22550125 | C2 | semidirect |
| 6. #22550123 | C2 | semidirect |
| 7. #22550080 | C2 | semidirect |
| 8. #22550077 | C2 | semidirect |
| 9. #22550076 | C2 | semidirect |
| 10. #22549898 | C2 | semidirect |
| 11. #477×C127 | C2 | semidirect |
| 138. C127 | #3254 | semidirect |
| 142. #477 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550430 | 2 |
| #22550427 | 2 |
| #22550168 | 2 |
| #22550155 | 2 |
| #22550125 | 2 |
| #22550123 | 2 |
| #22550080 | 2 |
| #22550077 | 2 |
| #22550076 | 2 |
| #22549898 | 2 |
| #477×C127 | 2 |
| #3254 | 127 |