Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#20263291 | C2 | semidirect |
| 4. #27161385 | C2 | semidirect |
| 5. #27161304 | C2 | semidirect |
| 6. #27161234 | C2 | semidirect |
| 8. #27161183 | C2 | semidirect |
| 9. #27161178 | C2 | semidirect |
| 10. #27161133 | C2 | semidirect |
| 11. #484×C197 | C2 | semidirect |
| 131. C197 | #3117 | semidirect |
| 135. #484 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161615 | 2 |
| C2×#20263291 | 2 |
| #27161397 | 2 |
| #27161385 | 2 |
| #27161304 | 2 |
| #27161234 | 2 |
| #27161220 | 2 |
| #27161183 | 2 |
| #27161178 | 2 |
| #27161133 | 2 |
| #484×C197 | 2 |
| #3117 | 197 |