Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
264 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. #27161063 | C2 | semidirect |
| 2. #27161053 | C2 | semidirect |
| 3. #27160869 | C2 | semidirect |
| 4. #27160866 | C2 | semidirect |
| 13. C23×C4×C197 | C4 | semidirect |
| 14. #123×C197 | C4 | semidirect |
| 18. #120×C197 | C4 | semidirect |
| 22. #117×C197 | C4 | semidirect |
| 114. C197 | #2120 | semidirect |
| 122. C23×C4 | Dic197 | semidirect |
| 124. #123 | Dic197 | semidirect |
| 128. #120 | Dic197 | semidirect |
| 133. #117 | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161063 | 2 |
| #27161053 | 2 |
| #27160869 | 2 |
| #27160866 | 2 |
| #525×C197 | 2 |
| #2120 | 197 |