Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×Dic1604 | C2 | semidirect |
| 3. C2×#20264354 | C2 | semidirect |
| 4. #27165717 | C2 | semidirect |
| 5. #27165660 | C2 | semidirect |
| 6. #27165649 | C2 | semidirect |
| 7. #102×C401 | C2 | semidirect |
| 60. C401 | #452 | semidirect |
| 67. #102 | D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264365 | 2 |
| C2×Dic1604 | 2 |
| C2×#20264354 | 2 |
| #27165717 | 2 |
| #27165660 | 2 |
| #27165649 | 2 |
| #102×C401 | 2 |
| #452 | 401 |