Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 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. #27160901 | C2 | semidirect |
| 4. #27160895 | C2 | semidirect |
| 6. #27160857 | C2 | semidirect |
| 7. #441×C197 | C2 | semidirect |
| 10. #20263272 | C4 | semidirect |
| 11. #20263269 | C4 | semidirect |
| 64. C197 | #2180 | semidirect |
| 68. #441 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161520 | 2 |
| #27161202 | 2 |
| #27160901 | 2 |
| #27160895 | 2 |
| #27160888 | 2 |
| #27160857 | 2 |
| #441×C197 | 2 |
| #2180 | 197 |