Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27161290 | C2 | semidirect |
| 5. #27160809 | C2 | semidirect |
| 6. #27160809 | C2 | semidirect |
| 90. C197 | #1640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161815 | 2 |
| #27161425 | 2 |
| #27161365 | 2 |
| #27161290 | 2 |
| #27160809 | 2 |
| #331×C197 | 2 |
| #1640 | 197 |