Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
736 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 8. C22×Dic254 | C4 | semidirect |
| 29. C22×Dic127 | Q8 | semidirect |
| 39. C22×C4×C127 | Q8 | semidirect |
| 97. C127 | #1446 | semidirect |
| 136. C22×C4 | Dic254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic254 | 2 |
| C2×C127⋊#95 | 2 |
| C2×#95×C127 | 2 |
| #1446 | 127 |