Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 69 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. #27161484 | C2 | semidirect |
| 2. #27161477 | C2 | semidirect |
| 5. #27161430 | C2 | semidirect |
| 7. #322×C197 | C2 | semidirect |
| 54. C8×C197 | SD16 | semidirect |
| 69. C197 | #1714 | semidirect |
| 77. #322 | D197 | semidirect |
| 124. C8 | #15691347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161484 | 2 |
| #27161477 | 2 |
| #27161452 | 2 |
| #27161430 | 2 |
| #27161426 | 2 |
| #322×C197 | 2 |
| #1714 | 197 |