Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #27161893 | C2 | semidirect |
| 2. #27161890 | C2 | semidirect |
| 3. #27161462 | C2 | semidirect |
| 4. #27161354 | C2 | semidirect |
| 5. #27161346 | C2 | semidirect |
| 6. #27161340 | C2 | semidirect |
| 7. #27161257 | C2 | semidirect |
| 8. #27161250 | C2 | semidirect |
| 9. #27161196 | C2 | semidirect |
| 10. #27161194 | C2 | semidirect |
| 11. #576×C197 | C2 | semidirect |
| 12. #20263373 | C22 | semidirect |
| 15. #20263356 | C22 | semidirect |
| 18. #20263352 | C22 | semidirect |
| 22. C2×Dic788 | C22 | semidirect |
| 25. C2×#15691346 | C22 | semidirect |
| 26. #20263333 | C22 | semidirect |
| 27. #20263332 | C22 | semidirect |
| 28. #20263313 | C22 | semidirect |
| 29. #20263262 | C22 | semidirect |
| 30. #20263261 | C22 | semidirect |
| 32. #20263253 | C22 | semidirect |
| 33. #20263252 | C22 | semidirect |
| 34. #20263244 | C22 | semidirect |
| 35. #20263243 | C22 | semidirect |
| 36. C8×Dic197 | C22 | semidirect |
| 149. C197 | #3290 | semidirect |
| 153. #576 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161893 | 2 |
| #27161890 | 2 |
| #27161462 | 2 |
| #27161354 | 2 |
| #27161346 | 2 |
| #27161340 | 2 |
| #27161257 | 2 |
| #27161250 | 2 |
| #27161196 | 2 |
| #27161194 | 2 |
| #576×C197 | 2 |
| #3290 | 197 |