Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
928 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 405 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 |
|---|---|---|
| 3. #22549783 | C2 | direct (N × H) |
| 15. C22×Q8×C127 | C4 | semidirect |
| 23. C22×Dic127 | Q8 | semidirect |
| 32. C2×Q8×C127 | C2×C4 | semidirect |
| 47. C2×Dic127 | C2×Q8 | semidirect |
| 77. C2×C127 | #391 | semidirect |
| 84. C127 | C2×#391 | semidirect |
| 92. C22×Q8 | Dic127 | semidirect |
| 107. C2×Q8 | C2×Dic127 | semidirect |
| 161. C2 | #22549783 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic127 | 2 |
| C22×C4×Dic127 | 2 |
| #22549783 | 2 |
| C2×C127⋊#95 | 2 |
| C23×Q8×C127 | 2 |
| C2×#391 | 127 |