Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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. #27161489 | C2 | semidirect |
| 4. #27161488 | C2 | semidirect |
| 5. #27161485 | C2 | semidirect |
| 6. #27161480 | C2 | semidirect |
| 7. #27161479 | C2 | semidirect |
| 11. #501×C197 | C2 | semidirect |
| 49. #15691341 | Q8 | semidirect |
| 121. C197 | #3166 | semidirect |
| 128. #501 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| #125×D197 | 2 |
| #27161489 | 2 |
| #27161488 | 2 |
| #27161485 | 2 |
| #27161480 | 2 |
| #27161479 | 2 |
| #27161120 | 2 |
| #27161118 | 2 |
| #27161031 | 2 |
| #501×C197 | 2 |
| #3166 | 197 |