Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27161453 | C2 | semidirect |
| 3. #27161366 | C2 | semidirect |
| 4. #27160822 | C2 | semidirect |
| 5. Q8⋊#13096802 | C2 | semidirect |
| 6. #27160806 | C2 | semidirect |
| 7. #477×C197 | C2 | semidirect |
| 69. Q8×C197 | SD16 | semidirect |
| 98. C197 | #1631 | semidirect |
| 102. #477 | D197 | semidirect |
| 153. Q8 | #15691345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161751 | 2 |
| #27161453 | 2 |
| #27161366 | 2 |
| #27160822 | 2 |
| Q8⋊#13096802 | 2 |
| #27160806 | 2 |
| #477×C197 | 2 |
| #1631 | 197 |