Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
180 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22549628 | C2 | semidirect |
| 4. #22549626 | C2 | semidirect |
| 19. #14523232 | C8 | semidirect |
| 36. C127⋊C8 | C2×C8 | semidirect |
| 67. C127 | #1565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549929 | 2 |
| C4×#14523232 | 2 |
| #22549628 | 2 |
| #22549626 | 2 |
| C2×C4⋊C8×C127 | 2 |
| #1565 | 127 |