Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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. #27160946 | C2 | semidirect |
| 3. #27160945 | C2 | semidirect |
| 6. C4⋊C4×Dic197 | C2 | semidirect |
| 8. #27160924 | C2 | semidirect |
| 9. #382×C197 | C2 | semidirect |
| 19. C42×D197 | C4 | semidirect |
| 105. C197 | #2283 | semidirect |
| 110. #382 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D197 | 2 |
| #27160946 | 2 |
| #27160945 | 2 |
| #27160941 | 2 |
| #27160936 | 2 |
| C4⋊C4×Dic197 | 2 |
| #27160926 | 2 |
| #27160924 | 2 |
| #382×C197 | 2 |
| #2283 | 197 |