Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
154 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22550316 | C2 | semidirect |
| 3. #22550260 | C2 | semidirect |
| 4. #22549697 | C2 | semidirect |
| 5. #22549691 | C2 | semidirect |
| 6. #22549688 | C2 | semidirect |
| 7. #443×C127 | C2 | semidirect |
| 75. C127 | #2212 | semidirect |
| 79. #443 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550316 | 2 |
| #22550311 | 2 |
| #22550260 | 2 |
| #22549697 | 2 |
| #22549691 | 2 |
| #22549688 | 2 |
| #443×C127 | 2 |
| #2212 | 127 |