Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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. #27161562 | C2 | semidirect |
| 2. #27161400 | C2 | semidirect |
| 3. #27161400 | C2 | semidirect |
| 4. #27161395 | C2 | semidirect |
| 5. #27161390 | C2 | semidirect |
| 6. #27161122 | C2 | semidirect |
| 7. #27161115 | C2 | semidirect |
| 8. #27161084 | C2 | semidirect |
| 9. C2×#20263247 | C2 | semidirect |
| 10. #27161046 | C2 | semidirect |
| 18. #20263285 | C22 | semidirect |
| 20. C2×C4⋊Dic197 | C22 | semidirect |
| 21. #20263259 | C22 | semidirect |
| 22. #20263259 | C22 | semidirect |
| 23. #20263259 | C22 | semidirect |
| 24. #20263257 | C22 | semidirect |
| 25. #20263257 | C22 | semidirect |
| 26. #20263257 | C22 | semidirect |
| 31. C22⋊#13096802 | C22 | semidirect |
| 32. C22⋊#13096802 | C22 | semidirect |
| 134. C197 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161562 | 2 |
| #27161400 | 2 |
| #27161395 | 2 |
| #27161390 | 2 |
| #27161122 | 2 |
| #27161115 | 2 |
| #27161084 | 2 |
| C2×#20263247 | 2 |
| #27161046 | 2 |
| #535×C197 | 2 |
| #3096 | 197 |