Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22549627 | C2 | semidirect |
| 36. C8×C127 | M16 | semidirect |
| 52. C127 | #1566 | semidirect |
| 88. C8 | #14523232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549900 | 2 |
| #22549627 | 2 |
| C2×C4×C8×C127 | 2 |
| #1566 | 127 |