Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22550180 | C2 | semidirect |
| 3. #22550180 | C2 | semidirect |
| 4. #22550168 | C2 | semidirect |
| 5. #22550158 | C2 | semidirect |
| 43. 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 |
|---|---|
| #22550353 | 2 |
| #22550180 | 2 |
| #22550168 | 2 |
| #22550158 | 2 |
| #22549916 | 2 |
| #22549912 | 2 |
| #22549903 | 2 |
| #22549884 | 2 |
| C2×#16861132 | 2 |
| #544×C127 | 2 |
| #3082 | 127 |