Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 65. Dic127 | Q32 | semidirect |
| 70. C127 | #2209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861155 | 2 |
| #22550254 | 2 |
| Q16×Dic127 | 2 |
| Dic127⋊C16 | 2 |
| #22549681 | 2 |
| #22549680 | 2 |
| C2×Q32×C127 | 2 |
| #2209 | 127 |