Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
190 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22549902 | C2 | semidirect |
| 5. #22549647 | C2 | semidirect |
| 6. #22549633 | C2 | semidirect |
| 7. #341×C127 | C2 | semidirect |
| 90. C127 | #2080 | semidirect |
| 96. #341 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549902 | 2 |
| #22549892 | 2 |
| #22549873 | 2 |
| #22549858 | 2 |
| #22549647 | 2 |
| #22549633 | 2 |
| #341×C127 | 2 |
| #2080 | 127 |