Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#20263346 | C2 | semidirect |
| 2. #27161750 | C2 | semidirect |
| 3. #27161455 | C2 | semidirect |
| 4. #27161313 | C2 | semidirect |
| 5. #27161279 | C2 | semidirect |
| 6. #27161276 | C2 | semidirect |
| 7. #27161224 | C2 | semidirect |
| 8. #27161222 | C2 | semidirect |
| 9. C4×#15691348 | C2 | semidirect |
| 10. D4×#13096802 | C2 | semidirect |
| 11. #550×C197 | C2 | semidirect |
| 51. #15691348 | D4 | semidirect |
| 131. C4×C197 | #135 | semidirect |
| 142. C197 | #3287 | semidirect |
| 146. #550 | D197 | semidirect |
| 276. C4 | #20263346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263346 | 2 |
| #27161750 | 2 |
| #27161455 | 2 |
| #27161313 | 2 |
| #27161279 | 2 |
| #27161276 | 2 |
| #27161224 | 2 |
| #27161222 | 2 |
| C4×#15691348 | 2 |
| D4×#13096802 | 2 |
| #550×C197 | 2 |
| #3287 | 197 |