Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22550507 | C2 | semidirect |
| 3. #22550182 | C2 | semidirect |
| 4. #22550179 | C2 | semidirect |
| 5. #22550170 | C2 | semidirect |
| 6. #22550155 | C2 | semidirect |
| 7. #22549916 | C2 | semidirect |
| 8. #22549902 | C2 | semidirect |
| 11. C2×#107×C127 | C2 | semidirect |
| 42. #14523248 | Q8 | semidirect |
| 124. C127 | #3083 | semidirect |
| 132. C2×#107 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550507 | 2 |
| #22550357 | 2 |
| #22550182 | 2 |
| #22550179 | 2 |
| #22550170 | 2 |
| #22550155 | 2 |
| #22549916 | 2 |
| #22549902 | 2 |
| #22549875 | 2 |
| #22549873 | 2 |
| C2×#107×C127 | 2 |
| #3083 | 127 |