Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27161431 | C2 | semidirect |
| 2. #27161429 | C2 | semidirect |
| 6. C8×#13096802 | C2 | semidirect |
| 7. #487×C197 | C2 | semidirect |
| 67. C197 | #1711 | semidirect |
| 71. #487 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161431 | 2 |
| #27161429 | 2 |
| #27161427 | 2 |
| #27161426 | 2 |
| C8×#13096802 | 2 |
| #487×C197 | 2 |
| #1711 | 197 |