Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22550280 | C2 | semidirect |
| 3. #22549678 | C2 | semidirect |
| 4. #22549677 | C2 | semidirect |
| 5. #22549676 | C2 | semidirect |
| 6. C16×Dic127 | C2 | semidirect |
| 7. #357×C127 | C2 | semidirect |
| 73. C127 | #2240 | semidirect |
| 79. #357 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550280 | 2 |
| #22550251 | 2 |
| #22549678 | 2 |
| #22549677 | 2 |
| #22549676 | 2 |
| C16×Dic127 | 2 |
| #357×C127 | 2 |
| #2240 | 127 |