Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 11. #16861208 | C4 | semidirect |
| 35. C4⋊Dic127 | Q8 | semidirect |
| 49. C4⋊C4×C127 | Q8 | semidirect |
| 103. C127 | #1987 | semidirect |
| 149. C4⋊C4 | Dic254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861208 | 2 |
| C2×Dic127⋊C8 | 2 |
| C4⋊C4×Dic127 | 2 |
| #22549639 | 2 |
| #22549638 | 2 |
| #340×C127 | 2 |
| #1987 | 127 |