Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 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. C4×C127⋊C8 | C4 | semidirect |
| 13. C4×C8×C127 | C4 | semidirect |
| 17. C4×Dic127 | C8 | semidirect |
| 59. C127 | #1274 | semidirect |
| 70. C4×C8 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549929 | 2 |
| #22549722 | 2 |
| #431×C127 | 2 |
| #1274 | 127 |