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 |
|---|---|---|
| 1. #22550255 | C2 | semidirect |
| 4. #22549628 | C2 | semidirect |
| 5. #22549622 | C2 | semidirect |
| 6. #22549621 | C2 | semidirect |
| 53. D4×C127 | Q16 | semidirect |
| 79. C127 | #1669 | semidirect |
| 127. D4 | #14523238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550255 | 2 |
| #22550156 | 2 |
| D4×C127⋊C8 | 2 |
| #22549628 | 2 |
| #22549622 | 2 |
| #22549621 | 2 |
| #474×C127 | 2 |
| #1669 | 127 |