Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 255 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 |
|---|---|---|
| 3. #22549904 | C2 | semidirect |
| 4. #22549902 | C2 | semidirect |
| 5. #22549899 | C2 | semidirect |
| 6. C2×Dic127⋊C8 | C2 | semidirect |
| 75. Dic127 | #131 | semidirect |
| 81. C127 | #2906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861216 | 2 |
| #41×Dic127 | 2 |
| #22549904 | 2 |
| #22549902 | 2 |
| #22549899 | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×#131×C127 | 2 |
| #2906 | 127 |