Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22550280 | C2 | semidirect |
| 3. #22549703 | C2 | semidirect |
| 4. Dic127⋊C16 | C2 | semidirect |
| 7. #367×C127 | C2 | semidirect |
| 23. D1016 | Q8 | semidirect |
| 64. C127 | #2226 | semidirect |
| 68. #367 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550280 | 2 |
| #22549958 | 2 |
| #22549703 | 2 |
| Dic127⋊C16 | 2 |
| #22549678 | 2 |
| #22549676 | 2 |
| #367×C127 | 2 |
| #2226 | 127 |