Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 2. Q8×Dic401 | C2 | semidirect |
| 4. #27165670 | C2 | semidirect |
| 6. #27165647 | C2 | semidirect |
| 7. #103×C401 | C2 | semidirect |
| 10. #20264353 | C4 | semidirect |
| 27. #15691999 | C2×C4 | semidirect |
| 29. Q8×C401 | C2×C4 | semidirect |
| 49. C401 | #440 | semidirect |
| 55. #103 | D401 | semidirect |
| 72. Q8 | C4×D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264353 | 2 |
| Q8×Dic401 | 2 |
| #27165699 | 2 |
| #27165670 | 2 |
| #27165659 | 2 |
| #27165647 | 2 |
| #103×C401 | 2 |
| #440 | 401 |