Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
172 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22550158 | C2 | semidirect |
| 4. #22550000 | C2 | semidirect |
| 5. #22549626 | C2 | semidirect |
| 7. #332×C127 | C2 | semidirect |
| 44. Dic254 | SD16 | semidirect |
| 54. C127⋊C8 | SD16 | semidirect |
| 80. C127 | #1666 | semidirect |
| 86. #332 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550250 | 2 |
| #22550158 | 2 |
| #22550077 | 2 |
| #22550000 | 2 |
| #22549626 | 2 |
| #22549619 | 2 |
| #332×C127 | 2 |
| #1666 | 127 |