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. #27161790 | C2 | semidirect |
| 3. #27161427 | C2 | semidirect |
| 4. #27161399 | C2 | semidirect |
| 5. #27161309 | C2 | semidirect |
| 6. #27161280 | C2 | semidirect |
| 7. #27161231 | C2 | semidirect |
| 8. C4×#15691346 | C2 | semidirect |
| 9. #27161144 | C2 | semidirect |
| 10. #102×D197 | C2 | semidirect |
| 11. #476×C197 | C2 | semidirect |
| 14. C2×#15691347 | C22 | semidirect |
| 16. C2×C8×D197 | C22 | semidirect |
| 19. #20263306 | C22 | semidirect |
| 24. C4×Dic394 | C22 | semidirect |
| 27. C4⋊C4×D197 | C22 | semidirect |
| 28. #20263257 | C22 | semidirect |
| 29. #20263249 | C22 | semidirect |
| 30. #20263248 | C22 | semidirect |
| 32. #20263246 | C22 | semidirect |
| 33. #20263246 | C22 | semidirect |
| 34. #20263238 | C22 | semidirect |
| 35. C4×#13096802 | C22 | semidirect |
| 36. C4⋊Q8×C197 | C22 | semidirect |
| 38. #106×C197 | C22 | semidirect |
| 39. C4⋊C8×C197 | C22 | semidirect |
| 89. D788 | SD16 | semidirect |
| 136. C197 | #3295 | semidirect |
| 142. #476 | D197 | semidirect |
| 154. C4⋊Q8 | C2×D197 | semidirect |
| 168. #106 | C2×D197 | semidirect |
| 169. C4⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161790 | 2 |
| D4×D788 | 2 |
| #27161427 | 2 |
| #27161399 | 2 |
| #27161309 | 2 |
| #27161280 | 2 |
| #27161231 | 2 |
| C4×#15691346 | 2 |
| #27161144 | 2 |
| #102×D197 | 2 |
| #476×C197 | 2 |
| #3295 | 197 |