Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #27161630 | C2 | semidirect |
| 2. C4×#15691359 | C2 | semidirect |
| 3. #27161405 | C2 | semidirect |
| 4. #27161356 | C2 | semidirect |
| 5. #27161279 | C2 | semidirect |
| 6. #27161275 | C2 | semidirect |
| 7. #27161227 | C2 | semidirect |
| 8. #27161190 | C2 | semidirect |
| 9. #27161182 | C2 | semidirect |
| 10. #27161135 | C2 | semidirect |
| 11. #475×C197 | C2 | semidirect |
| 93. D788 | #41 | semidirect |
| 109. Q8×C197 | #41 | semidirect |
| 144. C197 | #3115 | semidirect |
| 149. #475 | D197 | semidirect |
| 233. Q8 | #15691359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161630 | 2 |
| C4×#15691359 | 2 |
| #27161405 | 2 |
| #27161356 | 2 |
| #27161279 | 2 |
| #27161275 | 2 |
| #27161227 | 2 |
| #27161190 | 2 |
| #27161182 | 2 |
| #27161135 | 2 |
| #475×C197 | 2 |
| #3115 | 197 |