Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D127 | C2 | semidirect |
| 4. #22550087 | C2 | semidirect |
| 5. #22550085 | C2 | semidirect |
| 6. #22550083 | C2 | semidirect |
| 7. #22550081 | C2 | semidirect |
| 8. #22550079 | C2 | semidirect |
| 9. #22549898 | C2 | semidirect |
| 10. #22549883 | C2 | semidirect |
| 11. #461×C127 | C2 | semidirect |
| 131. C4×C127 | #137 | semidirect |
| 139. Dic127 | #137 | semidirect |
| 146. C127 | #3039 | semidirect |
| 155. #461 | D127 | semidirect |
| 283. C4 | #16861238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861238 | 2 |
| C4⋊Q8×D127 | 2 |
| C4×#14523247 | 2 |
| #22550087 | 2 |
| #22550085 | 2 |
| #22550083 | 2 |
| #22550081 | 2 |
| #22550079 | 2 |
| #22549898 | 2 |
| #22549883 | 2 |
| #461×C127 | 2 |
| #3039 | 127 |