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 |
|---|---|---|
| 1. #22550433 | C2 | semidirect |
| 3. #22550218 | C2 | semidirect |
| 4. #22550172 | C2 | semidirect |
| 5. #22550167 | C2 | semidirect |
| 6. #22550087 | C2 | semidirect |
| 7. #22550082 | C2 | semidirect |
| 9. #22549984 | C2 | semidirect |
| 10. #22549978 | C2 | semidirect |
| 11. #432×C127 | C2 | semidirect |
| 137. C127 | #3116 | semidirect |
| 148. #432 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550433 | 2 |
| C4×#14523248 | 2 |
| #22550218 | 2 |
| #22550172 | 2 |
| #22550167 | 2 |
| #22550087 | 2 |
| #22550082 | 2 |
| #22550040 | 2 |
| #22549984 | 2 |
| #22549978 | 2 |
| #432×C127 | 2 |
| #3116 | 127 |