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. #27160943 | C2 | semidirect |
| 6. C4×#15691337 | C2 | semidirect |
| 8. #27160925 | C2 | semidirect |
| 9. #376×C197 | C2 | semidirect |
| 19. C42×D197 | C4 | semidirect |
| 98. C197 | #2283 | semidirect |
| 108. #376 | 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 |
| #27160943 | 2 |
| #27160941 | 2 |
| #27160938 | 2 |
| C4×#15691337 | 2 |
| C4×#15691335 | 2 |
| #27160925 | 2 |
| #376×C197 | 2 |
| #2283 | 197 |