Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 4. #27161363 | C2 | semidirect |
| 5. #27161288 | C2 | semidirect |
| 8. #27161185 | C2 | semidirect |
| 9. #27161183 | C2 | semidirect |
| 127. C197 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161631 | 2 |
| C2×#20263291 | 2 |
| #27161409 | 2 |
| #27161363 | 2 |
| #27161288 | 2 |
| #27161237 | 2 |
| #27161234 | 2 |
| #27161185 | 2 |
| #27161183 | 2 |
| #27161133 | 2 |
| #483×C197 | 2 |
| #3113 | 197 |