Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
740 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 237 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. #22549756 | C2 | semidirect |
| 4. #22549742 | C2 | semidirect |
| 5. #22549722 | C2 | semidirect |
| 18. #127×C127 | C4 | semidirect |
| 29. C4×Dic127 | D4 | semidirect |
| 34. C2×D4×C127 | C2×C4 | semidirect |
| 35. C2×D4×C127 | C2×C4 | semidirect |
| 38. C42×C127 | C2×C4 | semidirect |
| 79. C127 | #2328 | semidirect |
| 89. #127 | Dic127 | semidirect |
| 103. C2×D4 | C2×Dic127 | semidirect |
| 104. C2×D4 | C2×Dic127 | semidirect |
| 117. C42 | C2×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 |
| #22549756 | 2 |
| #22549742 | 2 |
| #22549722 | 2 |
| C2×#127×C127 | 2 |
| #2328 | 127 |