Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 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. Q8×Dic254 | C2 | semidirect |
| 4. #22550227 | C2 | semidirect |
| 6. #22550162 | C2 | semidirect |
| 8. #22550087 | C2 | semidirect |
| 9. #22549984 | C2 | semidirect |
| 11. #446×C127 | C2 | semidirect |
| 117. C127 | #3369 | semidirect |
| 126. #446 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic254 | 2 |
| #22550599 | 2 |
| #22550236 | 2 |
| #22550227 | 2 |
| #22550167 | 2 |
| #22550162 | 2 |
| #22550099 | 2 |
| #22550087 | 2 |
| #22549984 | 2 |
| C4×#14523237 | 2 |
| #446×C127 | 2 |
| #3369 | 127 |