Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #27161559 | C2 | semidirect |
| 3. #27161402 | C2 | semidirect |
| 4. #27161401 | C2 | semidirect |
| 5. #27161396 | C2 | semidirect |
| 6. #27161391 | C2 | semidirect |
| 7. #27161121 | C2 | semidirect |
| 8. #27161115 | C2 | semidirect |
| 9. C2×#20263247 | C2 | semidirect |
| 10. #27161047 | C2 | semidirect |
| 11. #418×C197 | C2 | semidirect |
| 23. #20263284 | C22 | semidirect |
| 25. C4⋊C4×D197 | C22 | semidirect |
| 26. #20263260 | C22 | semidirect |
| 27. #20263259 | C22 | semidirect |
| 28. #20263259 | C22 | semidirect |
| 29. #20263258 | C22 | semidirect |
| 30. #20263257 | C22 | semidirect |
| 31. #20263257 | C22 | semidirect |
| 34. #20263238 | C22 | semidirect |
| 35. #20263238 | C22 | semidirect |
| 134. C197 | #3096 | semidirect |
| 144. #418 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161646 | 2 |
| #27161559 | 2 |
| #27161402 | 2 |
| #27161401 | 2 |
| #27161396 | 2 |
| #27161391 | 2 |
| #27161121 | 2 |
| #27161115 | 2 |
| C2×#20263247 | 2 |
| #27161047 | 2 |
| #418×C197 | 2 |
| #3096 | 197 |