Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 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×#20263356 | C2 | semidirect |
| 2. C22×#15691347 | C2 | semidirect |
| 4. #27161556 | C2 | semidirect |
| 5. #27161304 | C2 | semidirect |
| 6. #27161278 | C2 | semidirect |
| 7. #27161105 | C2 | semidirect |
| 8. #27161083 | C2 | semidirect |
| 9. #416×C197 | C2 | semidirect |
| 13. C2×#15691348 | C22 | semidirect |
| 16. C2×#15691346 | C22 | semidirect |
| 23. #20263291 | C22 | semidirect |
| 26. #20263255 | C22 | semidirect |
| 31. #103×C197 | C22 | semidirect |
| 32. #102×C197 | C22 | semidirect |
| 36. C2×Dic394 | D4 | semidirect |
| 116. C197 | #3043 | semidirect |
| 126. #416 | D197 | semidirect |
| 147. #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×#20263356 | 2 |
| C22×#15691347 | 2 |
| #27161643 | 2 |
| #27161556 | 2 |
| #27161304 | 2 |
| #27161278 | 2 |
| #27161105 | 2 |
| #27161083 | 2 |
| #416×C197 | 2 |
| #3043 | 197 |