Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #27165762 | C2 | semidirect |
| 2. C2×#20264351 | C2 | semidirect |
| 3. #27165744 | C2 | semidirect |
| 4. #27165672 | C2 | semidirect |
| 5. #27165654 | C2 | semidirect |
| 6. #27165653 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C401 | C2 | semidirect |
| 53. C401 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27165762 | 2 |
| C2×#20264351 | 2 |
| #27165744 | 2 |
| #27165672 | 2 |
| #27165654 | 2 |
| #27165653 | 2 |
| AGL(1,ℤ/8)×C401 | 2 |
| #472 | 401 |