Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161441 | C2 | semidirect |
| 4. #27161439 | C2 | semidirect |
| 5. #27161438 | C2 | semidirect |
| 6. #27161435 | C2 | semidirect |
| 7. #27161432 | C2 | semidirect |
| 8. #27161086 | C2 | semidirect |
| 10. #27161031 | C2 | semidirect |
| 11. #489×C197 | C2 | semidirect |
| 15. #20263326 | C22 | semidirect |
| 16. #20263317 | C22 | semidirect |
| 30. #20263251 | C22 | semidirect |
| 31. #20263250 | C22 | semidirect |
| 32. #20263249 | C22 | semidirect |
| 36. #20263237 | C22 | semidirect |
| 37. C8×Dic197 | C22 | semidirect |
| 38. C4⋊Q8×C197 | C22 | semidirect |
| 40. #103×C197 | C22 | semidirect |
| 42. #97×C197 | C22 | semidirect |
| 138. C197 | #3140 | semidirect |
| 145. #489 | D197 | semidirect |
| 155. C4⋊Q8 | C2×D197 | semidirect |
| 174. #103 | C2×D197 | semidirect |
| 180. #97 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| #124×D197 | 2 |
| #27161441 | 2 |
| #27161439 | 2 |
| #27161438 | 2 |
| #27161435 | 2 |
| #27161432 | 2 |
| #27161086 | 2 |
| #27161082 | 2 |
| #27161031 | 2 |
| #489×C197 | 2 |
| #3140 | 197 |