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 |
|---|---|---|
| 1. #22550255 | C2 | semidirect |
| 5. #22549628 | C2 | semidirect |
| 6. #22549623 | C2 | semidirect |
| 7. #332×C127 | C2 | semidirect |
| 46. D508 | Q16 | semidirect |
| 79. C127 | #1669 | semidirect |
| 86. #332 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550255 | 2 |
| #22550157 | 2 |
| #22550153 | 2 |
| #22549941 | 2 |
| #22549628 | 2 |
| #22549623 | 2 |
| #332×C127 | 2 |
| #1669 | 127 |