Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20263352 | C2 | semidirect |
| 2. #27161646 | C2 | semidirect |
| 3. #27161554 | C2 | semidirect |
| 4. #27161292 | C2 | semidirect |
| 5. #27161272 | C2 | semidirect |
| 6. #27161105 | C2 | semidirect |
| 7. #27161084 | C2 | semidirect |
| 8. #27161076 | C2 | semidirect |
| 9. C22×D8×C197 | C2 | semidirect |
| 12. C2×#15691346 | C22 | semidirect |
| 13. C2×#15691343 | C22 | semidirect |
| 15. #20263322 | C22 | semidirect |
| 16. #20263313 | C22 | semidirect |
| 20. D4×Dic197 | C22 | semidirect |
| 24. #20263255 | C22 | semidirect |
| 25. #20263251 | C22 | semidirect |
| 26. #20263248 | C22 | semidirect |
| 27. #20263247 | C22 | semidirect |
| 60. C2×D4×C197 | D4 | semidirect |
| 121. C197 | #3041 | semidirect |
| 124. C22×D8 | D197 | semidirect |
| 168. C2×D4 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263352 | 2 |
| #27161646 | 2 |
| #27161554 | 2 |
| #27161292 | 2 |
| #27161272 | 2 |
| #27161105 | 2 |
| #27161084 | 2 |
| #27161076 | 2 |
| C22×D8×C197 | 2 |
| #3041 | 197 |