Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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. C4×Dic802 | C2 | semidirect |
| 3. #27165670 | C2 | semidirect |
| 4. #27165660 | C2 | semidirect |
| 6. #27165648 | C2 | semidirect |
| 9. #20264354 | C4 | semidirect |
| 21. Dic802 | C2×C4 | semidirect |
| 25. #15691999 | C2×C4 | semidirect |
| 49. C401 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264354 | 2 |
| C4×Dic802 | 2 |
| #27165670 | 2 |
| #27165660 | 2 |
| #27165658 | 2 |
| #27165648 | 2 |
| C4×D4×C401 | 2 |
| #440 | 401 |