Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 4. C2×C8×Dic127 | C2 | semidirect |
| 5. #22549640 | C2 | semidirect |
| 6. #22549635 | C2 | semidirect |
| 7. #424×C127 | C2 | semidirect |
| 13. #16861132 | C4 | semidirect |
| 14. #16861129 | C4 | semidirect |
| 91. C127 | #1937 | semidirect |
| 92. #424 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861135 | 2 |
| #22549870 | 2 |
| #22549842 | 2 |
| C2×C8×Dic127 | 2 |
| #22549640 | 2 |
| #22549635 | 2 |
| #424×C127 | 2 |
| #1937 | 127 |