Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. #22549925 | C2 | semidirect |
| 2. #22549924 | C2 | semidirect |
| 3. #22549924 | C2 | semidirect |
| 6. C127⋊#338 | C2 | semidirect |
| 86. C127 | #2069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549925 | 2 |
| #22549924 | 2 |
| C2×#16861126 | 2 |
| C127⋊#338 | 2 |
| C2×#100×C127 | 2 |
| #2069 | 127 |