Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
372 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 135 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. C127⋊#338 | C2 | semidirect |
| 3. #338×C127 | C2 | semidirect |
| 53. D127 | #338 | direct (N × H) |
| 55. C127 | C2×#338 | semidirect |
| 58. #338 | D127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D127 | 2 |
| C127⋊#338 | 2 |
| #338×C127 | 2 |
| C2×#338 | 127 |