Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 1. C2×C22⋊(C127⋊C8) | C2 | semidirect |
| 3. C22×C127⋊C8 | C22 | semidirect |
| 12. C24×C127 | C8 | semidirect |
| 41. C22×C127 | C22⋊C8 | semidirect |
| 52. C127 | #1779 | semidirect |
| 63. C24 | C127⋊C8 | semidirect |
| 93. C22 | C22⋊(C127⋊C8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C127⋊C8) | 2 |
| C24×C4×C127 | 2 |
| #1779 | 127 |