Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22550600 | C2 | semidirect |
| 3. #22550228 | C2 | semidirect |
| 4. #22550219 | C2 | semidirect |
| 5. #22550118 | C2 | semidirect |
| 6. #22550087 | C2 | semidirect |
| 7. #22550039 | C2 | semidirect |
| 8. C4×#14523236 | C2 | semidirect |
| 9. #22549941 | C2 | semidirect |
| 10. #22549869 | C2 | semidirect |
| 11. #474×C127 | C2 | semidirect |
| 126. C127 | #3302 | semidirect |
| 131. #474 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550600 | 2 |
| #22550530 | 2 |
| #22550228 | 2 |
| #22550219 | 2 |
| #22550118 | 2 |
| #22550087 | 2 |
| #22550039 | 2 |
| C4×#14523236 | 2 |
| #22549941 | 2 |
| #22549869 | 2 |
| #474×C127 | 2 |
| #3302 | 127 |