Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
924 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 289 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×D4×Dic127 | C2 | semidirect |
| 2. #22549779 | C2 | semidirect |
| 3. #22549746 | C2 | semidirect |
| 4. C42×Dic127 | C2 | semidirect |
| 13. #127×C127 | C4 | semidirect |
| 22. C4×Dic127 | D4 | semidirect |
| 26. C2×D4×C127 | C2×C4 | semidirect |
| 28. C42×C127 | C2×C4 | semidirect |
| 48. C4×C127 | C4×D4 | semidirect |
| 51. Dic127 | #127 | direct (N × H) |
| 57. C127 | C4×#127 | semidirect |
| 65. #127 | Dic127 | direct (N × H) |
| 75. C2×D4 | C2×Dic127 | semidirect |
| 85. C42 | C2×Dic127 | semidirect |
| 108. C4 | D4×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic127 | 2 |
| #22549779 | 2 |
| #22549746 | 2 |
| C42×Dic127 | 2 |
| C2×#127×C127 | 2 |
| C4×#127 | 127 |