Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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. #27161629 | C2 | semidirect |
| 2. #27161369 | C2 | semidirect |
| 3. #27161366 | C2 | semidirect |
| 4. #27161330 | C2 | semidirect |
| 5. #27161274 | C2 | semidirect |
| 6. #27161271 | C2 | semidirect |
| 7. #27161103 | C2 | semidirect |
| 8. #532×C197 | C2 | semidirect |
| 120. C197 | #3253 | semidirect |
| 123. #532 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161629 | 2 |
| #27161369 | 2 |
| #27161366 | 2 |
| #27161330 | 2 |
| #27161274 | 2 |
| #27161271 | 2 |
| #27161103 | 2 |
| #532×C197 | 2 |
| #3253 | 197 |