Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 200 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 |
|---|---|---|
| 2. #27161361 | C2 | semidirect |
| 4. #27160825 | C2 | semidirect |
| 5. #27160811 | C2 | semidirect |
| 7. #500×C197 | C2 | semidirect |
| 88. C197 | #1650 | semidirect |
| 91. #500 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161803 | 2 |
| #27161361 | 2 |
| #27161281 | 2 |
| #27160825 | 2 |
| #27160811 | 2 |
| #27160808 | 2 |
| #500×C197 | 2 |
| #1650 | 197 |