Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22550162 | C2 | semidirect |
| 4. #22550003 | C2 | semidirect |
| 5. #22549628 | C2 | semidirect |
| 6. #22549623 | C2 | semidirect |
| 51. C127⋊C8 | SD16 | semidirect |
| 80. C127 | #1686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550248 | 2 |
| #22550162 | 2 |
| #22550073 | 2 |
| #22550003 | 2 |
| #22549628 | 2 |
| #22549623 | 2 |
| #331×C127 | 2 |
| #1686 | 127 |