Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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. #27161634 | C2 | semidirect |
| 3. #27161378 | C2 | semidirect |
| 4. #27161377 | C2 | semidirect |
| 5. #27161366 | C2 | semidirect |
| 6. #27161360 | C2 | semidirect |
| 7. #27161359 | C2 | semidirect |
| 8. #27161118 | C2 | semidirect |
| 9. #27161101 | C2 | semidirect |
| 11. #476×C197 | C2 | semidirect |
| 15. #20263326 | C22 | semidirect |
| 16. #20263317 | C22 | semidirect |
| 30. #20263260 | C22 | semidirect |
| 31. #20263259 | C22 | semidirect |
| 32. #20263257 | C22 | semidirect |
| 33. C4⋊#13096802 | C22 | semidirect |
| 34. #20263255 | C22 | semidirect |
| 38. C4⋊Q8×C197 | C22 | semidirect |
| 40. #106×C197 | C22 | semidirect |
| 41. C4⋊C8×C197 | C22 | semidirect |
| 48. D4×D197 | Q8 | semidirect |
| 144. C197 | #3077 | semidirect |
| 151. #476 | D197 | semidirect |
| 161. C4⋊Q8 | C2×D197 | semidirect |
| 180. #106 | C2×D197 | semidirect |
| 183. C4⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| C4×D4×D197 | 2 |
| #27161378 | 2 |
| #27161377 | 2 |
| #27161366 | 2 |
| #27161360 | 2 |
| #27161359 | 2 |
| #27161118 | 2 |
| #27161101 | 2 |
| #27161082 | 2 |
| #476×C197 | 2 |
| #3077 | 197 |