Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27161053 | C2 | semidirect |
| 3. #27160870 | C2 | semidirect |
| 4. #27160867 | C2 | semidirect |
| 5. #413×C197 | C2 | semidirect |
| 6. C22×C4×D197 | C4 | semidirect |
| 7. #20263307 | C4 | semidirect |
| 11. #20263294 | C4 | semidirect |
| 16. #20263285 | C4 | semidirect |
| 114. C197 | #2120 | semidirect |
| 117. #413 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161586 | 2 |
| #27161053 | 2 |
| #27160870 | 2 |
| #27160867 | 2 |
| #413×C197 | 2 |
| #2120 | 197 |