Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22550223 | C2 | semidirect |
| 3. #22550157 | C2 | semidirect |
| 4. #22550086 | C2 | semidirect |
| 5. #22549619 | C2 | semidirect |
| 6. #22549605 | C2 | semidirect |
| 7. Q8⋊C8×C127 | C2 | semidirect |
| 100. C127 | #1641 | semidirect |
| 106. Q8⋊C8 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550548 | 2 |
| #22550223 | 2 |
| #22550157 | 2 |
| #22550086 | 2 |
| #22549619 | 2 |
| #22549605 | 2 |
| Q8⋊C8×C127 | 2 |
| #1641 | 127 |