Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#20263357 | C2 | semidirect |
| 3. C2×#20263315 | C2 | semidirect |
| 4. #27161547 | C2 | semidirect |
| 5. #27161304 | C2 | semidirect |
| 6. #27161297 | C2 | semidirect |
| 7. #27161102 | C2 | semidirect |
| 8. #27161083 | C2 | semidirect |
| 9. #419×C197 | C2 | semidirect |
| 14. C2×#15691348 | C22 | semidirect |
| 16. C2×#15691345 | C22 | semidirect |
| 22. #20263291 | C22 | semidirect |
| 23. #20263288 | C22 | semidirect |
| 29. #20263255 | C22 | semidirect |
| 34. #103×C197 | C22 | semidirect |
| 125. C197 | #3040 | semidirect |
| 134. #419 | D197 | semidirect |
| 159. #103 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263357 | 2 |
| C2×#20263354 | 2 |
| C2×#20263315 | 2 |
| #27161547 | 2 |
| #27161304 | 2 |
| #27161297 | 2 |
| #27161102 | 2 |
| #27161083 | 2 |
| #419×C197 | 2 |
| #3040 | 197 |