Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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×#20263357 | C2 | semidirect |
| 3. C2×Q8×Dic197 | C2 | semidirect |
| 4. #27161303 | C2 | semidirect |
| 5. #27161299 | C2 | semidirect |
| 6. #27161287 | C2 | semidirect |
| 7. #27161277 | C2 | semidirect |
| 8. #27161102 | C2 | semidirect |
| 9. #27161081 | C2 | semidirect |
| 10. #27161080 | C2 | semidirect |
| 11. C2×#137×C197 | C2 | semidirect |
| 80. C2×Q8×C197 | D4 | semidirect |
| 150. Dic197 | #137 | semidirect |
| 157. C197 | #3037 | semidirect |
| 160. C2×#137 | D197 | semidirect |
| 210. C2×Q8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263357 | 2 |
| #27161625 | 2 |
| C2×Q8×Dic197 | 2 |
| #27161303 | 2 |
| #27161299 | 2 |
| #27161287 | 2 |
| #27161277 | 2 |
| #27161102 | 2 |
| #27161081 | 2 |
| #27161080 | 2 |
| C2×#137×C197 | 2 |
| #3037 | 197 |