Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22550693 | C2 | semidirect |
| 2. #22550690 | C2 | semidirect |
| 3. #22550256 | C2 | semidirect |
| 4. #22550152 | C2 | semidirect |
| 5. #22550151 | C2 | semidirect |
| 6. #22550060 | C2 | semidirect |
| 7. #22549994 | C2 | semidirect |
| 8. #443×C127 | C2 | semidirect |
| 100. C127 | #3293 | semidirect |
| 108. #443 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550693 | 2 |
| #22550690 | 2 |
| #22550256 | 2 |
| #22550152 | 2 |
| #22550151 | 2 |
| #22550060 | 2 |
| #22549994 | 2 |
| #443×C127 | 2 |
| #3293 | 127 |