Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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. D8×Dic127 | C2 | semidirect |
| 3. #22549958 | C2 | semidirect |
| 4. #22549701 | C2 | semidirect |
| 5. #22549678 | C2 | semidirect |
| 6. C16×Dic127 | C2 | semidirect |
| 7. #357×C127 | C2 | semidirect |
| 11. #16861150 | C4 | semidirect |
| 24. D1016 | C2×C4 | semidirect |
| 30. C127⋊C16 | C2×C4 | semidirect |
| 33. D8×C127 | C2×C4 | semidirect |
| 65. Dic127 | D16 | semidirect |
| 72. C127 | C4×D16 | semidirect |
| 78. #357 | D127 | semidirect |
| 99. D8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861150 | 2 |
| D8×Dic127 | 2 |
| #22549958 | 2 |
| #22549701 | 2 |
| #22549678 | 2 |
| C16×Dic127 | 2 |
| #357×C127 | 2 |
| C4×D16 | 127 |