Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22550431 | C2 | semidirect |
| 3. #22550216 | C2 | semidirect |
| 4. #22550172 | C2 | semidirect |
| 5. #22550166 | C2 | semidirect |
| 6. #22550083 | C2 | semidirect |
| 8. #22549980 | C2 | semidirect |
| 9. #22549977 | C2 | semidirect |
| 10. #22549932 | C2 | semidirect |
| 11. #461×C127 | C2 | semidirect |
| 137. C127 | #3116 | semidirect |
| 144. #461 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550431 | 2 |
| C4×#14523247 | 2 |
| #22550216 | 2 |
| #22550172 | 2 |
| #22550166 | 2 |
| #22550083 | 2 |
| #22550035 | 2 |
| #22549980 | 2 |
| #22549977 | 2 |
| #22549932 | 2 |
| #461×C127 | 2 |
| #3116 | 127 |