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. #27161627 | C2 | semidirect |
| 2. C4×#15691359 | C2 | semidirect |
| 3. #27161401 | C2 | semidirect |
| 4. #27161364 | C2 | semidirect |
| 5. #27161360 | C2 | semidirect |
| 6. #27161271 | C2 | semidirect |
| 7. #27161223 | C2 | semidirect |
| 8. #27161188 | C2 | semidirect |
| 9. #27161180 | C2 | semidirect |
| 10. #27161135 | C2 | semidirect |
| 11. #460×C197 | C2 | semidirect |
| 88. D788 | #41 | semidirect |
| 106. Q8×C197 | #41 | semidirect |
| 144. C197 | #3115 | semidirect |
| 151. #460 | D197 | semidirect |
| 233. Q8 | #15691357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161627 | 2 |
| C4×#15691359 | 2 |
| #27161401 | 2 |
| #27161364 | 2 |
| #27161360 | 2 |
| #27161271 | 2 |
| #27161223 | 2 |
| #27161188 | 2 |
| #27161180 | 2 |
| #27161135 | 2 |
| #460×C197 | 2 |
| #3115 | 197 |