Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 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 |
|---|---|---|
| 11. #97×C127 | C4 | semidirect |
| 12. C4×C8×C127 | C4 | semidirect |
| 53. C127 | #1841 | semidirect |
| 64. #97 | Dic127 | semidirect |
| 65. C4×C8 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549647 | 2 |
| #22549636 | 2 |
| C127⋊#338 | 2 |
| #22549633 | 2 |
| C4×M16×C127 | 2 |
| #1841 | 127 |