Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27161877 | C2 | semidirect |
| 2. C2×#20263354 | C2 | semidirect |
| 3. C2×#20263351 | C2 | semidirect |
| 4. #27161845 | C2 | semidirect |
| 5. #27161348 | C2 | semidirect |
| 6. #27161345 | C2 | semidirect |
| 7. #27161127 | C2 | semidirect |
| 8. C2×#20263242 | C2 | semidirect |
| 9. #413×C197 | C2 | semidirect |
| 12. #20263357 | C22 | semidirect |
| 16. #20263352 | C22 | semidirect |
| 22. C2×#15691345 | C22 | semidirect |
| 24. C2×#15691343 | C22 | semidirect |
| 25. #20263334 | C22 | semidirect |
| 30. #20263261 | C22 | semidirect |
| 31. #20263242 | C22 | semidirect |
| 35. #101×C197 | C22 | semidirect |
| 36. #100×C197 | C22 | semidirect |
| 147. C197 | #3068 | semidirect |
| 156. #413 | D197 | semidirect |
| 182. #101 | C2×D197 | semidirect |
| 184. #100 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161877 | 2 |
| C2×#20263354 | 2 |
| C2×#20263351 | 2 |
| #27161845 | 2 |
| #27161348 | 2 |
| #27161345 | 2 |
| #27161127 | 2 |
| C2×#20263242 | 2 |
| #413×C197 | 2 |
| #3068 | 197 |