Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 7. C22⋊(C127⋊C8) | C4 | semidirect |
| 13. C22⋊C8×C127 | C4 | semidirect |
| 18. C22×Dic127 | C8 | semidirect |
| 86. C127 | #1280 | semidirect |
| 97. C22⋊C8 | Dic127 | 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 |
| C2×C127⋊#95 | 2 |
| C2×C22⋊C8×C127 | 2 |
| #1280 | 127 |