Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
262 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. C4×#14523232 | C2 | semidirect |
| 3. #22549603 | C2 | semidirect |
| 4. #431×C127 | C2 | semidirect |
| 81. C127 | #1484 | semidirect |
| 83. #431 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550426 | 2 |
| C4×#14523232 | 2 |
| #22549603 | 2 |
| #431×C127 | 2 |
| #1484 | 127 |