Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #27161558 | C2 | semidirect |
| 3. #27161191 | C2 | semidirect |
| 4. #27161187 | C2 | semidirect |
| 5. #27161185 | C2 | semidirect |
| 6. #27161170 | C2 | semidirect |
| 7. C4×#15691346 | C2 | semidirect |
| 8. #106×D197 | C2 | semidirect |
| 9. #27161077 | C2 | semidirect |
| 10. #27161036 | C2 | semidirect |
| 11. #442×C197 | C2 | semidirect |
| 13. #20263345 | C4 | semidirect |
| 41. #15691357 | C2×C4 | semidirect |
| 48. Dic788 | C2×C4 | semidirect |
| 49. #15691346 | C2×C4 | semidirect |
| 53. C8×D197 | C2×C4 | semidirect |
| 66. D8×C197 | C2×C4 | semidirect |
| 114. C197 | #2952 | semidirect |
| 119. #442 | D197 | semidirect |
| 167. D8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263345 | 2 |
| #27161558 | 2 |
| #27161191 | 2 |
| #27161187 | 2 |
| #27161185 | 2 |
| #27161170 | 2 |
| C4×#15691346 | 2 |
| #106×D197 | 2 |
| #27161077 | 2 |
| #27161036 | 2 |
| #442×C197 | 2 |
| #2952 | 197 |