Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1144 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 389 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 |
|---|---|---|
| 2. #22549739 | C2 | direct (N × H) |
| 3. C2×C127⋊#95 | C2 | semidirect |
| 8. C127⋊#95 | C22 | semidirect |
| 11. C23×C4×C127 | C4 | semidirect |
| 27. C22×C4×C127 | C2×C4 | semidirect |
| 59. C2×C127 | #381 | semidirect |
| 64. C127 | C2×#381 | semidirect |
| 72. C23×C4 | Dic127 | semidirect |
| 90. C22×C4 | C2×Dic127 | semidirect |
| 123. C2 | #22549739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic127 | 2 |
| #22549739 | 2 |
| C2×C127⋊#95 | 2 |
| C24×C4×C127 | 2 |
| C2×#381 | 127 |