Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161710 | C2 | semidirect |
| 3. #27161442 | C2 | semidirect |
| 4. #27161437 | C2 | semidirect |
| 5. #27161432 | C2 | semidirect |
| 6. #27161424 | C2 | semidirect |
| 7. #27161084 | C2 | semidirect |
| 8. #27161078 | C2 | semidirect |
| 9. #27161076 | C2 | semidirect |
| 10. #27161034 | C2 | semidirect |
| 11. C2×#102×C197 | C2 | semidirect |
| 15. #20263325 | C22 | semidirect |
| 18. #20263317 | C22 | semidirect |
| 26. #20263251 | C22 | semidirect |
| 27. #20263251 | C22 | semidirect |
| 28. #20263249 | C22 | semidirect |
| 29. #20263248 | C22 | semidirect |
| 30. #20263248 | C22 | semidirect |
| 33. #20263246 | C22 | semidirect |
| 34. #20263236 | C22 | semidirect |
| 35. C8×Dic197 | C22 | semidirect |
| 135. C197 | #3136 | semidirect |
| 146. C2×#102 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161710 | 2 |
| #27161646 | 2 |
| #27161442 | 2 |
| #27161437 | 2 |
| #27161432 | 2 |
| #27161424 | 2 |
| #27161084 | 2 |
| #27161078 | 2 |
| #27161076 | 2 |
| #27161034 | 2 |
| C2×#102×C197 | 2 |
| #3136 | 197 |