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. #27161452 | C2 | semidirect |
| 3. #27161374 | C2 | semidirect |
| 4. #27161370 | C2 | semidirect |
| 5. #27160822 | C2 | semidirect |
| 6. #27160808 | C2 | semidirect |
| 7. Q8⋊C8×C197 | C2 | semidirect |
| 69. Q8×C197 | SD16 | semidirect |
| 98. C197 | #1631 | semidirect |
| 105. Q8⋊C8 | D197 | semidirect |
| 153. Q8 | #15691347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161751 | 2 |
| #27161452 | 2 |
| #27161374 | 2 |
| #27161370 | 2 |
| #27160822 | 2 |
| #27160808 | 2 |
| Q8⋊C8×C197 | 2 |
| #1631 | 197 |