Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 266 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 |
|---|---|---|
| 2. C2×#16861137 | C2 | semidirect |
| 3. #22549858 | C2 | semidirect |
| 4. C127⋊#338 | C2 | semidirect |
| 5. #423×C127 | C2 | semidirect |
| 79. C127 | #2050 | semidirect |
| 81. #423 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550676 | 2 |
| C2×#16861137 | 2 |
| #22549858 | 2 |
| C127⋊#338 | 2 |
| #423×C127 | 2 |
| #2050 | 127 |