Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
504 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 193 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. #22549772 | C2 | semidirect |
| 4. #22549740 | C2 | semidirect |
| 5. C4⋊C4×Dic127 | C2 | semidirect |
| 7. #22549721 | C2 | semidirect |
| 9. #16861168 | C4 | semidirect |
| 95. C127 | #2346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861168 | 2 |
| #22549772 | 2 |
| #22549770 | 2 |
| #22549740 | 2 |
| C4⋊C4×Dic127 | 2 |
| C4×C22⋊Dic127 | 2 |
| #22549721 | 2 |
| #380×C127 | 2 |
| #2346 | 127 |