Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22550421 | C2 | semidirect |
| 2. #22550280 | C2 | semidirect |
| 3. #22550251 | C2 | semidirect |
| 4. #22550221 | C2 | semidirect |
| 5. #22550112 | C2 | semidirect |
| 6. #22550110 | C2 | semidirect |
| 7. D8×Dic127 | C2 | semidirect |
| 8. #22549958 | C2 | semidirect |
| 9. #22549956 | C2 | semidirect |
| 10. C2×C8×Dic127 | C2 | semidirect |
| 11. #466×C127 | C2 | semidirect |
| 82. C2×Dic127 | D8 | semidirect |
| 89. C127⋊C8 | #41 | semidirect |
| 101. C8×C127 | #41 | semidirect |
| 128. C127 | #3169 | semidirect |
| 135. #466 | D127 | semidirect |
| 229. C8 | #14523247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550421 | 2 |
| #22550280 | 2 |
| #22550251 | 2 |
| #22550221 | 2 |
| #22550112 | 2 |
| #22550110 | 2 |
| D8×Dic127 | 2 |
| #22549958 | 2 |
| #22549956 | 2 |
| C2×C8×Dic127 | 2 |
| #466×C127 | 2 |
| #3169 | 127 |