Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 1. #22550280 | C2 | semidirect |
| 3. #22549702 | C2 | semidirect |
| 4. #22549701 | C2 | semidirect |
| 5. Dic127⋊C16 | C2 | semidirect |
| 30. D8×C127 | Q8 | semidirect |
| 64. C127 | #2224 | semidirect |
| 87. D8 | Dic254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550280 | 2 |
| D8×Dic127 | 2 |
| #22549702 | 2 |
| #22549701 | 2 |
| Dic127⋊C16 | 2 |
| #22549677 | 2 |
| #357×C127 | 2 |
| #2224 | 127 |