Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27161615 | C2 | semidirect |
| 2. C2×D4×Dic197 | C2 | semidirect |
| 3. #27161407 | C2 | semidirect |
| 4. #27161393 | C2 | semidirect |
| 5. #27161377 | C2 | semidirect |
| 6. #27161296 | C2 | semidirect |
| 8. #27161188 | C2 | semidirect |
| 9. #27161180 | C2 | semidirect |
| 10. #27161133 | C2 | semidirect |
| 11. #450×C197 | C2 | semidirect |
| 15. #20263317 | C22 | semidirect |
| 16. #20263315 | C22 | semidirect |
| 19. Q8×Dic197 | C22 | semidirect |
| 24. #20263288 | C22 | semidirect |
| 30. #20263260 | C22 | semidirect |
| 31. #20263257 | C22 | semidirect |
| 32. #20263255 | C22 | semidirect |
| 33. #20263250 | C22 | semidirect |
| 34. #20263248 | C22 | semidirect |
| 37. #20263236 | C22 | semidirect |
| 140. C197 | #3114 | semidirect |
| 148. #450 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161615 | 2 |
| C2×D4×Dic197 | 2 |
| #27161407 | 2 |
| #27161393 | 2 |
| #27161377 | 2 |
| #27161296 | 2 |
| #27161213 | 2 |
| #27161188 | 2 |
| #27161180 | 2 |
| #27161133 | 2 |
| #450×C197 | 2 |
| #3114 | 197 |