Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 9. #16861119 | C4 | semidirect |
| 10. C4×C127⋊C8 | C4 | semidirect |
| 11. C8×Dic127 | C4 | semidirect |
| 15. #97×C127 | C4 | semidirect |
| 54. C127 | #1726 | semidirect |
| 66. #97 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861119 | 2 |
| C2×C4×C127⋊C8 | 2 |
| C2×C8×Dic127 | 2 |
| #22549722 | 2 |
| C2×#97×C127 | 2 |
| #1726 | 127 |