Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
752 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 325 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. C2×C4×Dic127 | C4 | semidirect |
| 8. C127⋊#95 | C4 | semidirect |
| 10. #95×C127 | C4 | semidirect |
| 31. C2×Dic127 | C42 | semidirect |
| 45. C2×C4×C127 | C42 | semidirect |
| 60. Dic127 | #95 | direct (N × H) |
| 69. C127 | C4×#95 | semidirect |
| 79. #95 | Dic127 | direct (N × H) |
| 114. C2×C4 | C4×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic127 | 2 |
| C2×C127⋊#95 | 2 |
| C2×#95×C127 | 2 |
| C4×#95 | 127 |