Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×#16861216 | C2 | semidirect |
| 3. #22549884 | C2 | semidirect |
| 4. #22549875 | C2 | semidirect |
| 5. #22549870 | C2 | semidirect |
| 6. C2×#16861132 | C2 | semidirect |
| 7. #520×C127 | C2 | semidirect |
| 9. #16861256 | C4 | semidirect |
| 28. #14523248 | C2×C4 | semidirect |
| 32. C2×Dic254 | C2×C4 | semidirect |
| 95. C127 | #2898 | semidirect |
| 98. #520 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861256 | 2 |
| C2×#16861216 | 2 |
| #22549884 | 2 |
| #22549875 | 2 |
| #22549870 | 2 |
| C2×#16861132 | 2 |
| #520×C127 | 2 |
| #2898 | 127 |