Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 8. #16861128 | C4 | semidirect |
| 14. #101×C127 | C4 | semidirect |
| 77. C127 | #1394 | semidirect |
| 89. #101 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861128 | 2 |
| #22549783 | 2 |
| C2×#101×C127 | 2 |
| #1394 | 127 |