Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27161786 | C2 | semidirect |
| 2. #27161425 | C2 | semidirect |
| 3. #27161395 | C2 | semidirect |
| 4. #27161369 | C2 | semidirect |
| 5. #27161306 | C2 | semidirect |
| 6. #27161276 | C2 | semidirect |
| 7. #27161230 | C2 | semidirect |
| 8. C4×#15691346 | C2 | semidirect |
| 9. D4×#13096802 | C2 | semidirect |
| 10. C2×#20263247 | C2 | semidirect |
| 13. C2×#15691346 | C22 | semidirect |
| 14. C22×#13096802 | C22 | semidirect |
| 15. #20263326 | C22 | semidirect |
| 17. #20263305 | C22 | semidirect |
| 19. C4×Dic394 | C22 | semidirect |
| 21. C2×C4⋊Dic197 | C22 | semidirect |
| 22. #20263257 | C22 | semidirect |
| 23. #20263257 | C22 | semidirect |
| 24. C4⋊#13096802 | C22 | semidirect |
| 25. #20263249 | C22 | semidirect |
| 28. #20263247 | C22 | semidirect |
| 29. #20263247 | C22 | semidirect |
| 30. #20263247 | C22 | semidirect |
| 31. C22⋊#13096802 | C22 | semidirect |
| 32. C4×#13096802 | C22 | semidirect |
| 100. D4×C197 | SD16 | semidirect |
| 136. C197 | #3295 | semidirect |
| 230. D4 | #15691346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161786 | 2 |
| #27161425 | 2 |
| #27161395 | 2 |
| #27161369 | 2 |
| #27161306 | 2 |
| #27161276 | 2 |
| #27161230 | 2 |
| C4×#15691346 | 2 |
| D4×#13096802 | 2 |
| C2×#20263247 | 2 |
| D42×C197 | 2 |
| #3295 | 197 |