Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #22550599 | C2 | semidirect |
| 2. #22550586 | C2 | semidirect |
| 3. #22550231 | C2 | semidirect |
| 4. #22550227 | C2 | semidirect |
| 5. #22550184 | C2 | semidirect |
| 6. #22550167 | C2 | semidirect |
| 8. #22550082 | C2 | semidirect |
| 9. C4×#14523237 | C2 | semidirect |
| 11. C8×Q8×C127 | C2 | semidirect |
| 121. C127 | #3360 | semidirect |
| 130. C8×Q8 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550599 | 2 |
| #22550586 | 2 |
| #22550231 | 2 |
| #22550227 | 2 |
| #22550184 | 2 |
| #22550167 | 2 |
| #22550092 | 2 |
| #22550082 | 2 |
| C4×#14523237 | 2 |
| C4×D1016 | 2 |
| C8×Q8×C127 | 2 |
| #3360 | 127 |