Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 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. #22550541 | C2 | semidirect |
| 3. #22550224 | C2 | semidirect |
| 4. #22550221 | C2 | semidirect |
| 5. #22550155 | C2 | semidirect |
| 6. #22550072 | C2 | semidirect |
| 7. #22550070 | C2 | semidirect |
| 8. #22550000 | C2 | semidirect |
| 9. #22549958 | C2 | semidirect |
| 10. C4×#14523233 | C2 | semidirect |
| 11. #474×C127 | C2 | semidirect |
| 78. Dic254 | D8 | semidirect |
| 84. D508 | #41 | semidirect |
| 132. C127 | #3358 | semidirect |
| 138. #474 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550547 | 2 |
| #22550541 | 2 |
| #22550224 | 2 |
| #22550221 | 2 |
| #22550155 | 2 |
| #22550072 | 2 |
| #22550070 | 2 |
| #22550000 | 2 |
| #22549958 | 2 |
| C4×#14523233 | 2 |
| #474×C127 | 2 |
| #3358 | 127 |