Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #27161782 | C2 | semidirect |
| 2. #27161406 | C2 | semidirect |
| 3. #27161394 | C2 | semidirect |
| 4. #27161376 | C2 | semidirect |
| 5. #27161333 | C2 | semidirect |
| 6. C4×D1576 | C2 | semidirect |
| 7. #27161158 | C2 | semidirect |
| 8. #27161118 | C2 | semidirect |
| 9. #499×C197 | C2 | semidirect |
| 102. C197 | #3355 | semidirect |
| 105. #499 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161782 | 2 |
| #27161406 | 2 |
| #27161394 | 2 |
| #27161376 | 2 |
| #27161333 | 2 |
| C4×D1576 | 2 |
| #27161158 | 2 |
| #27161118 | 2 |
| #499×C197 | 2 |
| #3355 | 197 |