Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 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. C2×#16861150 | C2 | semidirect |
| 2. #22550251 | C2 | semidirect |
| 3. D8×Dic127 | C2 | semidirect |
| 4. Dic127⋊C16 | C2 | semidirect |
| 5. #22549678 | C2 | semidirect |
| 6. #22549677 | C2 | semidirect |
| 7. C2×D16×C127 | C2 | semidirect |
| 38. D8×C127 | D4 | semidirect |
| 74. Dic127 | D16 | semidirect |
| 82. C127 | #2206 | semidirect |
| 84. C2×D16 | D127 | semidirect |
| 115. D8 | C22⋊D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861150 | 2 |
| #22550251 | 2 |
| D8×Dic127 | 2 |
| Dic127⋊C16 | 2 |
| #22549678 | 2 |
| #22549677 | 2 |
| C2×D16×C127 | 2 |
| #2206 | 127 |