Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 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. #27161210 | C2 | semidirect |
| 4. #27160831 | C2 | semidirect |
| 5. #27160825 | C2 | semidirect |
| 7. #475×C197 | C2 | semidirect |
| 51. #13096802 | SD16 | semidirect |
| 79. C197 | #1686 | semidirect |
| 82. #475 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161453 | 2 |
| #27161279 | 2 |
| #27161210 | 2 |
| #27160831 | 2 |
| #27160825 | 2 |
| #27160822 | 2 |
| #475×C197 | 2 |
| #1686 | 197 |