Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
160 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×C127⋊C16 | C4 | semidirect |
| 14. C2×C16×C127 | C4 | semidirect |
| 32. C2×Dic127 | C16 | semidirect |
| 61. C127 | #1374 | semidirect |
| 73. C2×C16 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C127⋊C16 | 2 |
| C2×C8×Dic127 | 2 |
| C22×C16×C127 | 2 |
| #1374 | 127 |