Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
240 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 12. #16861119 | C4 | semidirect |
| 13. C8×Dic127 | C4 | semidirect |
| 82. C127 | #1746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861119 | 2 |
| C2×C8×Dic127 | 2 |
| #22549722 | 2 |
| #22549631 | 2 |
| #22549630 | 2 |
| #336×C127 | 2 |
| #1746 | 127 |