Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 3. #22550186 | C2 | semidirect |
| 4. #22550182 | C2 | semidirect |
| 5. #22550170 | C2 | semidirect |
| 6. #22550160 | C2 | semidirect |
| 44. C2×Dic254 | Q8 | semidirect |
| 117. C127 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550504 | 2 |
| #22550353 | 2 |
| #22550186 | 2 |
| #22550182 | 2 |
| #22550170 | 2 |
| #22550160 | 2 |
| #22549919 | 2 |
| #22549902 | 2 |
| #22549884 | 2 |
| C2×#16861134 | 2 |
| #427×C127 | 2 |
| #3082 | 127 |