Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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. #27161613 | C2 | semidirect |
| 2. C2×C4×D788 | C2 | semidirect |
| 3. #27161410 | C2 | semidirect |
| 4. #27161393 | C2 | semidirect |
| 5. #27161380 | C2 | semidirect |
| 6. #27161295 | C2 | semidirect |
| 7. #27161232 | C2 | semidirect |
| 9. #27161192 | C2 | semidirect |
| 10. #27161181 | C2 | semidirect |
| 11. #432×C197 | C2 | semidirect |
| 17. #20263318 | C22 | semidirect |
| 18. #20263314 | C22 | semidirect |
| 22. C4×Dic394 | C22 | semidirect |
| 27. C4×D788 | C22 | semidirect |
| 32. #20263260 | C22 | semidirect |
| 33. #20263258 | C22 | semidirect |
| 34. #20263251 | C22 | semidirect |
| 37. #20263248 | C22 | semidirect |
| 39. C4⋊C8×C197 | C22 | semidirect |
| 42. #97×C197 | C22 | semidirect |
| 140. C197 | #3114 | semidirect |
| 152. #432 | D197 | semidirect |
| 176. C4⋊C8 | C2×D197 | semidirect |
| 183. #97 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161613 | 2 |
| C2×C4×D788 | 2 |
| #27161410 | 2 |
| #27161393 | 2 |
| #27161380 | 2 |
| #27161295 | 2 |
| #27161232 | 2 |
| #27161215 | 2 |
| #27161192 | 2 |
| #27161181 | 2 |
| #432×C197 | 2 |
| #3114 | 197 |