Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22550572 | C2 | semidirect |
| 2. #22550278 | C2 | semidirect |
| 3. #22550201 | C2 | semidirect |
| 4. #22550190 | C2 | semidirect |
| 5. #22550177 | C2 | semidirect |
| 6. #22550129 | C2 | semidirect |
| 7. C4×D1016 | C2 | semidirect |
| 8. #22549918 | C2 | semidirect |
| 9. #436×C127 | C2 | semidirect |
| 103. C127 | #3355 | semidirect |
| 111. #436 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550572 | 2 |
| #22550278 | 2 |
| #22550201 | 2 |
| #22550190 | 2 |
| #22550177 | 2 |
| #22550129 | 2 |
| C4×D1016 | 2 |
| #22549918 | 2 |
| #436×C127 | 2 |
| #3355 | 127 |