Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #22550186 | C2 | semidirect |
| 4. #22550185 | C2 | semidirect |
| 5. #22550172 | C2 | semidirect |
| 6. #22550171 | C2 | semidirect |
| 7. #22550158 | C2 | semidirect |
| 11. #475×C127 | C2 | semidirect |
| 47. Q8×D127 | Q8 | semidirect |
| 131. C127 | #3078 | semidirect |
| 139. #475 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550431 | 2 |
| C4×Q8×D127 | 2 |
| #22550186 | 2 |
| #22550185 | 2 |
| #22550172 | 2 |
| #22550171 | 2 |
| #22550158 | 2 |
| #22549915 | 2 |
| #22549898 | 2 |
| #22549883 | 2 |
| #475×C127 | 2 |
| #3078 | 127 |