Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#15691347 | C2 | semidirect |
| 3. #27161650 | C2 | semidirect |
| 4. #27161553 | C2 | semidirect |
| 5. #27161293 | C2 | semidirect |
| 6. #27161283 | C2 | semidirect |
| 7. #27161105 | C2 | semidirect |
| 8. #27161087 | C2 | semidirect |
| 9. #416×C197 | C2 | semidirect |
| 18. #20263324 | C22 | semidirect |
| 19. #20263313 | C22 | semidirect |
| 26. #20263255 | C22 | semidirect |
| 27. #20263249 | C22 | semidirect |
| 31. #103×C197 | C22 | semidirect |
| 32. #102×C197 | C22 | semidirect |
| 116. C197 | #3042 | semidirect |
| 126. #416 | D197 | semidirect |
| 148. #103 | C2×D197 | semidirect |
| 149. #102 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| C22×#15691347 | 2 |
| #27161650 | 2 |
| #27161553 | 2 |
| #27161293 | 2 |
| #27161283 | 2 |
| #27161105 | 2 |
| #27161087 | 2 |
| #416×C197 | 2 |
| #3042 | 197 |