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. #27161487 | C2 | semidirect |
| 4. #27161486 | C2 | semidirect |
| 5. #27161481 | C2 | semidirect |
| 6. #27161478 | C2 | semidirect |
| 7. #27161478 | C2 | semidirect |
| 11. #499×C197 | C2 | semidirect |
| 43. #15691341 | Q8 | semidirect |
| 44. #15691341 | Q8 | semidirect |
| 99. C197 | #3166 | semidirect |
| 108. #499 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161635 | 2 |
| #125×D197 | 2 |
| #27161487 | 2 |
| #27161486 | 2 |
| #27161481 | 2 |
| #27161478 | 2 |
| #27161120 | 2 |
| #27161118 | 2 |
| C4×#15691341 | 2 |
| #499×C197 | 2 |
| #3166 | 197 |