Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1144 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 349 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. #22549737 | C2 | direct (N × H) |
| 4. C2×C127⋊#95 | C2 | semidirect |
| 8. C23×Dic127 | C4 | semidirect |
| 14. C127⋊#95 | C22 | semidirect |
| 27. C22×Dic127 | C2×C4 | semidirect |
| 82. C2×C127 | #381 | semidirect |
| 88. C127 | C2×#381 | semidirect |
| 170. C2 | #22549737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic127 | 2 |
| C22×C22⋊Dic127 | 2 |
| #22549737 | 2 |
| C2×C127⋊#95 | 2 |
| C22×C22⋊C4×C127 | 2 |
| C2×#381 | 127 |