Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22550452 | C2 | semidirect |
| 3. C2×#16861197 | C2 | semidirect |
| 4. C2×#16861137 | C2 | semidirect |
| 5. #22549880 | C2 | semidirect |
| 6. C2×#16861127 | C2 | semidirect |
| 7. #339×C127 | C2 | semidirect |
| 131. C127 | #2003 | semidirect |
| 138. #339 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861237 | 2 |
| #22550452 | 2 |
| C2×#16861197 | 2 |
| C2×#16861137 | 2 |
| #22549880 | 2 |
| C2×#16861127 | 2 |
| #339×C127 | 2 |
| #2003 | 127 |