Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C2×Q8×Dic127 | C2 | semidirect |
| 3. #22550190 | C2 | semidirect |
| 4. #22550187 | C2 | semidirect |
| 5. #22550169 | C2 | semidirect |
| 6. #22550074 | C2 | semidirect |
| 7. #22550015 | C2 | semidirect |
| 8. #22549979 | C2 | semidirect |
| 9. #22549977 | C2 | semidirect |
| 10. #22549930 | C2 | semidirect |
| 11. #448×C127 | C2 | semidirect |
| 104. Q8×C127 | #41 | semidirect |
| 141. C127 | #3112 | semidirect |
| 149. #448 | D127 | semidirect |
| 229. Q8 | #14523247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550421 | 2 |
| C2×Q8×Dic127 | 2 |
| #22550190 | 2 |
| #22550187 | 2 |
| #22550169 | 2 |
| #22550074 | 2 |
| #22550015 | 2 |
| #22549979 | 2 |
| #22549977 | 2 |
| #22549930 | 2 |
| #448×C127 | 2 |
| #3112 | 127 |