Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #27161365 | C2 | semidirect |
| 4. #27161364 | C2 | semidirect |
| 5. #27161362 | C2 | semidirect |
| 8. #27161287 | C2 | semidirect |
| 9. #27161286 | C2 | semidirect |
| 11. #462×C197 | C2 | semidirect |
| 129. C197 | #3255 | semidirect |
| 140. #462 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| #27161633 | 2 |
| #27161365 | 2 |
| #27161364 | 2 |
| #27161362 | 2 |
| #27161336 | 2 |
| #27161334 | 2 |
| #27161287 | 2 |
| #27161286 | 2 |
| #27161101 | 2 |
| #462×C197 | 2 |
| #3255 | 197 |