Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 72. C127 | #1680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550228 | 2 |
| #22550161 | 2 |
| Q8×C127⋊C8 | 2 |
| #22549626 | 2 |
| #22549622 | 2 |
| #22549621 | 2 |
| #462×C127 | 2 |
| #1680 | 127 |