Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22550611 | C2 | semidirect |
| 2. #22550265 | C2 | semidirect |
| 3. #22550260 | C2 | semidirect |
| 4. #22550099 | C2 | semidirect |
| 5. #22550092 | C2 | semidirect |
| 6. #22550072 | C2 | semidirect |
| 7. #22549978 | C2 | semidirect |
| 8. C4×D1016 | C2 | semidirect |
| 9. #446×C127 | C2 | semidirect |
| 109. C127 | #3403 | semidirect |
| 116. #446 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550611 | 2 |
| #22550265 | 2 |
| #22550260 | 2 |
| #22550099 | 2 |
| #22550092 | 2 |
| #22550072 | 2 |
| #22549978 | 2 |
| C4×D1016 | 2 |
| #446×C127 | 2 |
| #3403 | 127 |