Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. D4×Dic254 | C2 | semidirect |
| 3. #22550223 | C2 | semidirect |
| 4. #22550221 | C2 | semidirect |
| 5. #22550156 | C2 | semidirect |
| 6. #22550155 | C2 | semidirect |
| 7. #22550071 | C2 | semidirect |
| 8. #22550069 | C2 | semidirect |
| 9. C8×Dic254 | C2 | semidirect |
| 10. #22549956 | C2 | semidirect |
| 11. C4×D8×C127 | C2 | semidirect |
| 78. Dic254 | D8 | semidirect |
| 96. D4×C127 | #41 | semidirect |
| 132. C127 | #3358 | semidirect |
| 143. C4×D8 | D127 | semidirect |
| 222. D4 | #14523248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550547 | 2 |
| D4×Dic254 | 2 |
| #22550223 | 2 |
| #22550221 | 2 |
| #22550156 | 2 |
| #22550155 | 2 |
| #22550071 | 2 |
| #22550069 | 2 |
| C8×Dic254 | 2 |
| #22549956 | 2 |
| C4×D8×C127 | 2 |
| #3358 | 127 |