Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
312 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 9. C2×Dic508 | C4 | semidirect |
| 48. C2×Dic127 | Q16 | semidirect |
| 78. C127 | #1969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic508 | 2 |
| C2×#16861132 | 2 |
| C2×C8×Dic127 | 2 |
| #22549781 | 2 |
| C2×#107×C127 | 2 |
| #1969 | 127 |