Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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. #27189716 | C2 | semidirect |
| 2. #27189712 | C2 | semidirect |
| 3. #27189710 | C2 | semidirect |
| 5. #27189693 | C2 | semidirect |
| 6. Q8×Dic409 | C2 | semidirect |
| 7. #27189682 | C2 | semidirect |
| 9. #27189676 | C2 | semidirect |
| 10. #27189675 | C2 | semidirect |
| 11. C22⋊Q8×C409 | C2 | semidirect |
| 72. C409 | #556 | semidirect |
| 79. C22⋊Q8 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27189716 | 2 |
| #27189712 | 2 |
| #27189710 | 2 |
| #27189703 | 2 |
| #27189693 | 2 |
| Q8×Dic409 | 2 |
| #27189682 | 2 |
| C4×C22⋊D409 | 2 |
| #27189676 | 2 |
| #27189675 | 2 |
| C22⋊Q8×C409 | 2 |
| #556 | 409 |