Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20263346 | C2 | semidirect |
| 2. C22×#15691342 | C2 | semidirect |
| 3. #27161590 | C2 | semidirect |
| 4. #27161335 | C2 | semidirect |
| 5. #27161330 | C2 | semidirect |
| 6. #27161327 | C2 | semidirect |
| 7. #27161323 | C2 | semidirect |
| 8. #27161115 | C2 | semidirect |
| 9. #27161075 | C2 | semidirect |
| 10. #27161073 | C2 | semidirect |
| 11. #525×C197 | C2 | semidirect |
| 14. C2×#15691348 | C22 | semidirect |
| 15. C2×#15691346 | C22 | semidirect |
| 16. C2×#15691345 | C22 | semidirect |
| 17. C2×#15691343 | C22 | semidirect |
| 29. #20263259 | C22 | semidirect |
| 30. #20263257 | C22 | semidirect |
| 31. #20263250 | C22 | semidirect |
| 32. #20263249 | C22 | semidirect |
| 33. #20263247 | C22 | semidirect |
| 34. #20263246 | C22 | semidirect |
| 57. C2×#13096802 | D4 | semidirect |
| 148. C197 | #3054 | semidirect |
| 153. #525 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263346 | 2 |
| C22×#15691342 | 2 |
| #27161590 | 2 |
| #27161335 | 2 |
| #27161330 | 2 |
| #27161327 | 2 |
| #27161323 | 2 |
| #27161115 | 2 |
| #27161075 | 2 |
| #27161073 | 2 |
| #525×C197 | 2 |
| #3054 | 197 |