Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#20263354 | C2 | semidirect |
| 2. C2×#20263351 | C2 | semidirect |
| 3. #27161625 | C2 | semidirect |
| 4. C2×#20263288 | C2 | semidirect |
| 5. #27161297 | C2 | semidirect |
| 6. #27161293 | C2 | semidirect |
| 7. #27161283 | C2 | semidirect |
| 8. #27161273 | C2 | semidirect |
| 9. #27161102 | C2 | semidirect |
| 10. #27161078 | C2 | semidirect |
| 11. #417×C197 | C2 | semidirect |
| 22. #20263324 | C22 | semidirect |
| 23. #20263322 | C22 | semidirect |
| 24. #20263315 | C22 | semidirect |
| 25. #20263313 | C22 | semidirect |
| 36. #20263255 | C22 | semidirect |
| 37. #20263255 | C22 | semidirect |
| 38. #20263249 | C22 | semidirect |
| 39. #20263246 | C22 | semidirect |
| 43. #103×C197 | C22 | semidirect |
| 44. #102×C197 | C22 | semidirect |
| 51. C2×D788 | D4 | semidirect |
| 158. Dic197 | AGL(1,ℤ/8) | semidirect |
| 166. C197 | #3036 | semidirect |
| 178. #417 | D197 | semidirect |
| 209. #103 | C2×D197 | semidirect |
| 211. #102 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263354 | 2 |
| C2×#20263351 | 2 |
| #27161625 | 2 |
| C2×#20263288 | 2 |
| #27161297 | 2 |
| #27161293 | 2 |
| #27161283 | 2 |
| #27161273 | 2 |
| #27161102 | 2 |
| #27161078 | 2 |
| #417×C197 | 2 |
| #3036 | 197 |