Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
524 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 524 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 |
|---|---|---|
| 2. #22549762 | C2 | semidirect |
| 3. C4×C4⋊Dic127 | C2 | semidirect |
| 5. #22549722 | C2 | semidirect |
| 6. C42×Dic127 | C2 | semidirect |
| 17. #117×C127 | C4 | semidirect |
| 76. C127 | #2298 | semidirect |
| 85. #117 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549769 | 2 |
| #22549762 | 2 |
| C4×C4⋊Dic127 | 2 |
| C4×C22⋊Dic127 | 2 |
| #22549722 | 2 |
| C42×Dic127 | 2 |
| C2×#117×C127 | 2 |
| #2298 | 127 |