Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#20263348 | C2 | semidirect |
| 2. C2×#20263345 | C2 | semidirect |
| 3. #27161747 | C2 | semidirect |
| 4. #27161454 | C2 | semidirect |
| 5. #27161316 | C2 | semidirect |
| 6. #27161278 | C2 | semidirect |
| 7. #27161225 | C2 | semidirect |
| 8. #27161222 | C2 | semidirect |
| 9. #27161173 | C2 | semidirect |
| 10. C8×C22⋊D197 | C2 | semidirect |
| 11. #466×C197 | C2 | semidirect |
| 56. Dic788 | D4 | semidirect |
| 134. Dic197 | #135 | semidirect |
| 142. C197 | #3287 | semidirect |
| 149. #466 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263348 | 2 |
| C2×#20263345 | 2 |
| #27161747 | 2 |
| #27161454 | 2 |
| #27161316 | 2 |
| #27161278 | 2 |
| #27161225 | 2 |
| #27161222 | 2 |
| #27161173 | 2 |
| C8×C22⋊D197 | 2 |
| #466×C197 | 2 |
| #3287 | 197 |