Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 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. C2×#20263354 | C2 | semidirect |
| 2. C22×#15691343 | C2 | semidirect |
| 3. #27161646 | C2 | semidirect |
| 4. #27161553 | C2 | semidirect |
| 5. #27161293 | C2 | semidirect |
| 6. #27161273 | C2 | semidirect |
| 7. #27161107 | C2 | semidirect |
| 8. #27161073 | C2 | semidirect |
| 9. #418×C197 | C2 | semidirect |
| 13. C2×#15691347 | C22 | semidirect |
| 14. C2×D1576 | C22 | semidirect |
| 18. #20263322 | C22 | semidirect |
| 19. #20263313 | C22 | semidirect |
| 23. #20263288 | C22 | semidirect |
| 26. #20263255 | C22 | semidirect |
| 27. #20263249 | C22 | semidirect |
| 28. #20263246 | C22 | semidirect |
| 32. #102×C197 | C22 | semidirect |
| 39. C2×D788 | D4 | semidirect |
| 121. C197 | #3041 | semidirect |
| 130. #418 | D197 | semidirect |
| 154. #102 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263354 | 2 |
| C22×#15691343 | 2 |
| #27161646 | 2 |
| #27161553 | 2 |
| #27161293 | 2 |
| #27161273 | 2 |
| #27161107 | 2 |
| #27161073 | 2 |
| #418×C197 | 2 |
| #3041 | 197 |