Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 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. #27161803 | C2 | semidirect |
| 3. #27161482 | C2 | semidirect |
| 4. #27161416 | C2 | semidirect |
| 5. #27161402 | C2 | semidirect |
| 6. #27161365 | C2 | semidirect |
| 7. #27161324 | C2 | semidirect |
| 8. C4×#15691346 | C2 | semidirect |
| 9. #27161156 | C2 | semidirect |
| 10. #27161120 | C2 | semidirect |
| 11. #474×C197 | C2 | semidirect |
| 88. #13096802 | #41 | semidirect |
| 122. C197 | #3353 | semidirect |
| 130. #474 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161803 | 2 |
| #27161734 | 2 |
| #27161482 | 2 |
| #27161416 | 2 |
| #27161402 | 2 |
| #27161365 | 2 |
| #27161324 | 2 |
| C4×#15691346 | 2 |
| #27161156 | 2 |
| #27161120 | 2 |
| #474×C197 | 2 |
| #3353 | 197 |