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 |
| 3. #27161444 | C2 | semidirect |
| 4. #27161439 | C2 | semidirect |
| 5. #27161434 | C2 | semidirect |
| 6. #27161426 | C2 | semidirect |
| 7. #27161085 | C2 | semidirect |
| 8. #27161081 | C2 | semidirect |
| 9. #27161076 | C2 | semidirect |
| 10. C2×#20263248 | C2 | semidirect |
| 11. #405×C197 | C2 | semidirect |
| 14. #20263326 | C22 | semidirect |
| 17. #20263318 | C22 | semidirect |
| 26. #20263251 | C22 | semidirect |
| 27. #20263251 | C22 | semidirect |
| 28. #20263251 | C22 | semidirect |
| 33. #20263248 | C22 | semidirect |
| 34. #20263248 | C22 | semidirect |
| 35. #20263248 | C22 | semidirect |
| 39. #97×C197 | C22 | semidirect |
| 40. C4×C8×C197 | C22 | semidirect |
| 135. C197 | #3136 | semidirect |
| 147. #405 | D197 | semidirect |
| 175. #97 | C2×D197 | semidirect |
| 176. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161707 | 2 |
| #27161648 | 2 |
| #27161444 | 2 |
| #27161439 | 2 |
| #27161434 | 2 |
| #27161426 | 2 |
| #27161085 | 2 |
| #27161081 | 2 |
| #27161076 | 2 |
| C2×#20263248 | 2 |
| #405×C197 | 2 |
| #3136 | 197 |