Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. #22550547 | C2 | semidirect |
| 2. #22550224 | C2 | semidirect |
| 3. #22550200 | C2 | semidirect |
| 4. #22550168 | C2 | semidirect |
| 5. #22550110 | C2 | semidirect |
| 6. #22550071 | C2 | semidirect |
| 7. #22550019 | C2 | semidirect |
| 8. C4×#14523236 | C2 | semidirect |
| 9. D4×C127⋊C8 | C2 | semidirect |
| 10. #22549870 | C2 | semidirect |
| 11. #555×C127 | C2 | semidirect |
| 133. C127 | #3305 | semidirect |
| 134. #555 | 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 |
| #22550168 | 2 |
| #22550110 | 2 |
| #22550071 | 2 |
| #22550019 | 2 |
| C4×#14523236 | 2 |
| D4×C127⋊C8 | 2 |
| #22549870 | 2 |
| #555×C127 | 2 |
| #3305 | 127 |