Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161789 | C2 | semidirect |
| 3. #27161425 | C2 | semidirect |
| 4. #27161396 | C2 | semidirect |
| 5. #27161370 | C2 | semidirect |
| 6. #27161305 | C2 | semidirect |
| 7. #27161228 | C2 | semidirect |
| 8. C4×#15691345 | C2 | semidirect |
| 9. #27161144 | C2 | semidirect |
| 10. #102×D197 | C2 | semidirect |
| 11. #460×C197 | C2 | semidirect |
| 15. C2×C8×D197 | C22 | semidirect |
| 16. #20263326 | C22 | semidirect |
| 19. #20263302 | C22 | semidirect |
| 26. C4⋊C4×D197 | C22 | semidirect |
| 27. #20263258 | C22 | semidirect |
| 28. #20263257 | C22 | semidirect |
| 29. #20263250 | C22 | semidirect |
| 31. #20263247 | C22 | semidirect |
| 32. #20263247 | C22 | semidirect |
| 34. #20263238 | C22 | semidirect |
| 35. C4×#13096802 | C22 | semidirect |
| 36. C2×SD16×C197 | C22 | semidirect |
| 38. C4×Q8×C197 | C22 | semidirect |
| 39. C4⋊C8×C197 | C22 | semidirect |
| 40. #102×C197 | C22 | semidirect |
| 84. D788 | SD16 | semidirect |
| 136. C197 | #3295 | semidirect |
| 144. #460 | D197 | semidirect |
| 152. C2×SD16 | C2×D197 | semidirect |
| 162. C4×Q8 | C2×D197 | semidirect |
| 169. C4⋊C8 | C2×D197 | semidirect |
| 175. #102 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161789 | 2 |
| #27161714 | 2 |
| #27161425 | 2 |
| #27161396 | 2 |
| #27161370 | 2 |
| #27161305 | 2 |
| #27161228 | 2 |
| C4×#15691345 | 2 |
| #27161144 | 2 |
| #102×D197 | 2 |
| #460×C197 | 2 |
| #3295 | 197 |