Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
296 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 10. C4×C127⋊C8 | C4 | semidirect |
| 15. C4⋊C8×C127 | C4 | semidirect |
| 23. C4⋊Dic127 | C8 | semidirect |
| 38. C127⋊C8 | C4⋊C4 | semidirect |
| 57. C4×C127 | C4×C8 | semidirect |
| 69. C127 | C8×C4⋊C4 | semidirect |
| 81. C4⋊C8 | Dic127 | semidirect |
| 127. C4 | C8×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C127⋊C8 | 2 |
| C2×C8×Dic127 | 2 |
| C4×C4⋊Dic127 | 2 |
| #22549630 | 2 |
| C2×C4⋊C8×C127 | 2 |
| C8×C4⋊C4 | 127 |