Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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. #27161789 | C2 | semidirect |
| 3. #27161426 | C2 | semidirect |
| 4. #27161399 | C2 | semidirect |
| 5. #27161369 | C2 | semidirect |
| 6. #27161311 | C2 | semidirect |
| 7. #27161279 | C2 | semidirect |
| 8. #27161228 | C2 | semidirect |
| 9. C8×D788 | C2 | semidirect |
| 10. #102×D197 | C2 | semidirect |
| 11. C4×SD16×C197 | C2 | semidirect |
| 14. C2×#15691345 | C22 | semidirect |
| 15. C2×C8×D197 | C22 | semidirect |
| 16. #20263326 | C22 | semidirect |
| 20. #20263302 | C22 | semidirect |
| 26. C4⋊C4×D197 | C22 | semidirect |
| 27. #20263257 | C22 | semidirect |
| 28. C4⋊#13096802 | C22 | semidirect |
| 29. #20263248 | C22 | semidirect |
| 30. #20263248 | C22 | semidirect |
| 32. #20263246 | C22 | semidirect |
| 33. #20263238 | C22 | semidirect |
| 35. C4×Q8×C197 | C22 | semidirect |
| 37. #106×C197 | C22 | semidirect |
| 38. #103×C197 | C22 | semidirect |
| 40. C4×C8×C197 | C22 | semidirect |
| 88. D788 | SD16 | semidirect |
| 136. C197 | #3295 | semidirect |
| 146. C4×SD16 | D197 | semidirect |
| 162. C4×Q8 | C2×D197 | semidirect |
| 168. #106 | C2×D197 | semidirect |
| 170. #103 | C2×D197 | semidirect |
| 177. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161789 | 2 |
| D4×D788 | 2 |
| #27161426 | 2 |
| #27161399 | 2 |
| #27161369 | 2 |
| #27161311 | 2 |
| #27161279 | 2 |
| #27161228 | 2 |
| C8×D788 | 2 |
| #102×D197 | 2 |
| C4×SD16×C197 | 2 |
| #3295 | 197 |