Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22550605 | C2 | semidirect |
| 4. #22550227 | C2 | semidirect |
| 5. #22550186 | C2 | semidirect |
| 8. #22550086 | C2 | semidirect |
| 9. C8×Dic254 | C2 | semidirect |
| 10. #22549968 | C2 | semidirect |
| 116. C127 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550605 | 2 |
| #22550596 | 2 |
| #22550229 | 2 |
| #22550227 | 2 |
| #22550186 | 2 |
| #22550156 | 2 |
| #22550096 | 2 |
| #22550086 | 2 |
| C8×Dic254 | 2 |
| #22549968 | 2 |
| C4×SD16×C127 | 2 |
| #3364 | 127 |