Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22550214 | C2 | semidirect |
| 3. #22550168 | C2 | semidirect |
| 4. #22550163 | C2 | semidirect |
| 5. #22550083 | C2 | semidirect |
| 6. #22550078 | C2 | semidirect |
| 8. #22549981 | C2 | semidirect |
| 9. #22549974 | C2 | semidirect |
| 10. #22549933 | C2 | semidirect |
| 11. #533×C127 | C2 | semidirect |
| 137. C127 | #3116 | semidirect |
| 138. #533 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523248 | 2 |
| #22550214 | 2 |
| #22550168 | 2 |
| #22550163 | 2 |
| #22550083 | 2 |
| #22550078 | 2 |
| #22550036 | 2 |
| #22549981 | 2 |
| #22549974 | 2 |
| #22549933 | 2 |
| #533×C127 | 2 |
| #3116 | 127 |