Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #27161627 | C2 | semidirect |
| 2. #27161626 | C2 | semidirect |
| 3. #27161370 | C2 | semidirect |
| 4. #27161369 | C2 | semidirect |
| 5. #27161367 | C2 | semidirect |
| 6. #27161331 | C2 | semidirect |
| 7. #27161329 | C2 | semidirect |
| 8. #27161272 | C2 | semidirect |
| 9. #27161271 | C2 | semidirect |
| 10. #27161101 | C2 | semidirect |
| 11. #459×C197 | C2 | semidirect |
| 150. C197 | #3253 | semidirect |
| 161. #459 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161627 | 2 |
| #27161626 | 2 |
| #27161370 | 2 |
| #27161369 | 2 |
| #27161367 | 2 |
| #27161331 | 2 |
| #27161329 | 2 |
| #27161272 | 2 |
| #27161271 | 2 |
| #27161101 | 2 |
| #459×C197 | 2 |
| #3253 | 197 |