Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 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. D8×Dic127 | C2 | semidirect |
| 2. #22549702 | C2 | semidirect |
| 3. #22549677 | C2 | semidirect |
| 4. C16×Dic127 | C2 | semidirect |
| 12. D16×C127 | C4 | semidirect |
| 22. D8×C127 | C2×C4 | semidirect |
| 24. C16×C127 | C2×C4 | semidirect |
| 44. Dic127 | D16 | direct (N × H) |
| 50. C127 | C4×D16 | semidirect |
| 58. D16 | Dic127 | direct (N × H) |
| 67. D8 | C2×Dic127 | semidirect |
| 74. C16 | C2×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic127 | 2 |
| #22549702 | 2 |
| #22549677 | 2 |
| C16×Dic127 | 2 |
| C2×D16×C127 | 2 |
| C4×D16 | 127 |