Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #27161707 | C2 | semidirect |
| 2. #27161443 | C2 | semidirect |
| 3. #27161438 | C2 | semidirect |
| 4. #27161433 | C2 | semidirect |
| 5. #27161425 | C2 | semidirect |
| 6. #27161084 | C2 | semidirect |
| 7. #27161080 | C2 | semidirect |
| 8. #27161075 | C2 | semidirect |
| 9. C2×#20263247 | C2 | semidirect |
| 10. #27161035 | C2 | semidirect |
| 14. #20263326 | C22 | semidirect |
| 16. #20263318 | C22 | semidirect |
| 21. #20263250 | C22 | semidirect |
| 22. #20263250 | C22 | semidirect |
| 23. #20263250 | C22 | semidirect |
| 28. #20263247 | C22 | semidirect |
| 29. #20263247 | C22 | semidirect |
| 30. #20263247 | C22 | semidirect |
| 31. #20263237 | C22 | semidirect |
| 32. C4×#13096802 | C22 | semidirect |
| 135. C197 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161707 | 2 |
| #27161443 | 2 |
| #27161438 | 2 |
| #27161433 | 2 |
| #27161425 | 2 |
| #27161084 | 2 |
| #27161080 | 2 |
| #27161075 | 2 |
| C2×#20263247 | 2 |
| #27161035 | 2 |
| #535×C197 | 2 |
| #3136 | 197 |