Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 7. #16861120 | C4 | semidirect |
| 13. #97×C127 | C4 | semidirect |
| 61. C127 | #1295 | semidirect |
| 72. #97 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861120 | 2 |
| #22549742 | 2 |
| C2×#97×C127 | 2 |
| #1295 | 127 |