Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
840 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 405 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. #22549721 | C2 | direct (N × H) |
| 7. C2×C4×Dic127 | C4 | semidirect |
| 18. C4×Dic127 | C2×C4 | semidirect |
| 45. C2×C127 | #376 | semidirect |
| 50. C127 | C2×#376 | semidirect |
| 95. C2 | #22549721 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic127 | 2 |
| #22549721 | 2 |
| C2×C127⋊#95 | 2 |
| C2×#95×C127 | 2 |
| C2×#376 | 127 |