Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161423 | C2 | semidirect |
| 4. #27161422 | C2 | semidirect |
| 5. #27161416 | C2 | semidirect |
| 6. #27161411 | C2 | semidirect |
| 7. #27161122 | C2 | semidirect |
| 8. #27161087 | C2 | semidirect |
| 9. C2×#20263251 | C2 | semidirect |
| 11. #427×C197 | C2 | semidirect |
| 126. C197 | #3097 | semidirect |
| 135. #427 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161655 | 2 |
| #27161559 | 2 |
| #27161423 | 2 |
| #27161422 | 2 |
| #27161416 | 2 |
| #27161411 | 2 |
| #27161122 | 2 |
| #27161087 | 2 |
| C2×#20263251 | 2 |
| #27161045 | 2 |
| #427×C197 | 2 |
| #3097 | 197 |