Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C2×#20263346 | C2 | semidirect |
| 3. #27161643 | C2 | semidirect |
| 4. #27161560 | C2 | semidirect |
| 5. #27161304 | C2 | semidirect |
| 6. #27161297 | C2 | semidirect |
| 7. #27161278 | C2 | semidirect |
| 8. #27161273 | C2 | semidirect |
| 9. #27161107 | C2 | semidirect |
| 10. C2×#20263246 | C2 | semidirect |
| 11. #417×C197 | C2 | semidirect |
| 16. C2×#15691348 | C22 | semidirect |
| 18. C2×#15691346 | C22 | semidirect |
| 19. C2×#15691345 | C22 | semidirect |
| 21. C2×#15691343 | C22 | semidirect |
| 28. #20263291 | C22 | semidirect |
| 29. #20263288 | C22 | semidirect |
| 34. #20263255 | C22 | semidirect |
| 35. #20263255 | C22 | semidirect |
| 41. #103×C197 | C22 | semidirect |
| 42. #102×C197 | C22 | semidirect |
| 45. #15691358 | D4 | semidirect |
| 154. C197 | #3045 | semidirect |
| 165. #417 | D197 | semidirect |
| 194. #103 | C2×D197 | semidirect |
| 197. #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 |
| C2×#20263346 | 2 |
| #27161643 | 2 |
| #27161560 | 2 |
| #27161304 | 2 |
| #27161297 | 2 |
| #27161278 | 2 |
| #27161273 | 2 |
| #27161107 | 2 |
| C2×#20263246 | 2 |
| #417×C197 | 2 |
| #3045 | 197 |