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. #22550226 | C2 | semidirect |
| 5. #22550185 | C2 | semidirect |
| 8. #22550000 | C2 | semidirect |
| 9. Q16×Dic127 | C2 | semidirect |
| 11. #462×C127 | C2 | semidirect |
| 116. C127 | #3364 | semidirect |
| 124. #462 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550605 | 2 |
| #22550600 | 2 |
| #22550232 | 2 |
| #22550226 | 2 |
| #22550185 | 2 |
| #22550157 | 2 |
| #22550100 | 2 |
| #22550000 | 2 |
| Q16×Dic127 | 2 |
| C4×#14523235 | 2 |
| #462×C127 | 2 |
| #3364 | 127 |