Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22550224 | C2 | semidirect |
| 3. #22550200 | C2 | semidirect |
| 4. #22550158 | C2 | semidirect |
| 5. #22550107 | C2 | semidirect |
| 6. #22550076 | C2 | semidirect |
| 7. #22550036 | C2 | semidirect |
| 8. C4×#14523238 | C2 | semidirect |
| 9. D4×C127⋊C8 | C2 | semidirect |
| 10. #22549870 | C2 | semidirect |
| 11. #556×C127 | C2 | semidirect |
| 128. C127 | #3304 | semidirect |
| 129. #556 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550547 | 2 |
| #22550224 | 2 |
| #22550200 | 2 |
| #22550158 | 2 |
| #22550107 | 2 |
| #22550076 | 2 |
| #22550036 | 2 |
| C4×#14523238 | 2 |
| D4×C127⋊C8 | 2 |
| #22549870 | 2 |
| #556×C127 | 2 |
| #3304 | 127 |