Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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. C24×Dic197 | C2 | semidirect |
| 3. C2×#20263286 | C2 | semidirect |
| 4. #27160956 | C2 | semidirect |
| 5. #27160951 | C2 | semidirect |
| 6. C22⋊C4×Dic197 | C2 | semidirect |
| 7. #379×C197 | C2 | semidirect |
| 12. C22×C4×D197 | C22 | semidirect |
| 13. #20263295 | C4 | semidirect |
| 15. C2×#15691337 | C22 | semidirect |
| 17. C2×#15691335 | C22 | semidirect |
| 18. C2×C4×Dic197 | C22 | semidirect |
| 19. #20263233 | C22 | semidirect |
| 26. C2×C22⋊D197 | C2×C4 | semidirect |
| 31. C22×Dic197 | D4 | semidirect |
| 37. C22⋊Dic197 | C2×C4 | semidirect |
| 42. C24×C197 | C2×C4 | semidirect |
| 50. C22×D197 | C22×C4 | semidirect |
| 57. C2×Dic197 | C22×C4 | semidirect |
| 78. C22×C197 | C4×D4 | semidirect |
| 89. Dic197 | #120 | semidirect |
| 95. C197 | C4×#120 | semidirect |
| 102. #379 | D197 | semidirect |
| 122. C24 | C4×D197 | semidirect |
| 177. C22 | #20263286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic197 | 2 |
| C2×#20263295 | 2 |
| C2×#20263286 | 2 |
| #27160956 | 2 |
| #27160951 | 2 |
| C22⋊C4×Dic197 | 2 |
| #379×C197 | 2 |
| C4×#120 | 197 |