Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22550161 | C2 | semidirect |
| 3. Q8×C127⋊C8 | C2 | semidirect |
| 4. #22549626 | C2 | semidirect |
| 5. #22549621 | C2 | semidirect |
| 48. C127⋊C8 | SD16 | semidirect |
| 51. Q8×C127 | SD16 | semidirect |
| 80. C127 | #1666 | semidirect |
| 126. Q8 | #14523236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550248 | 2 |
| #22550161 | 2 |
| Q8×C127⋊C8 | 2 |
| #22549626 | 2 |
| #22549621 | 2 |
| #22549620 | 2 |
| #460×C127 | 2 |
| #1666 | 127 |