Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
752 conjugacy classes of subgroups; only the 421 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 421 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. C4×C4⋊Dic127 | C2 | semidirect |
| 4. #22549722 | C2 | semidirect |
| 5. C42×Dic127 | C2 | semidirect |
| 7. #16861168 | C4 | direct (N × H) |
| 15. C2×C42×C127 | C4 | semidirect |
| 20. C4⋊Dic127 | C2×C4 | semidirect |
| 23. C4×Dic127 | C2×C4 | semidirect |
| 44. C2×C4×C127 | C42 | semidirect |
| 61. C4×C127 | #117 | semidirect |
| 68. C127 | C4×#117 | semidirect |
| 82. C2×C42 | Dic127 | semidirect |
| 112. C2×C4 | C4×Dic127 | semidirect |
| 130. C4 | #16861168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861168 | 2 |
| C4×C4⋊Dic127 | 2 |
| C4×C22⋊Dic127 | 2 |
| #22549722 | 2 |
| C42×Dic127 | 2 |
| C22×C42×C127 | 2 |
| C4×#117 | 127 |