Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27161624 | C2 | semidirect |
| 2. C2×D4×Dic197 | C2 | semidirect |
| 3. #27161393 | C2 | semidirect |
| 4. #27161390 | C2 | semidirect |
| 5. #27161357 | C2 | semidirect |
| 6. #27161272 | C2 | semidirect |
| 7. #27161213 | C2 | semidirect |
| 8. D8×Dic197 | C2 | semidirect |
| 9. #27161159 | C2 | semidirect |
| 10. #27161129 | C2 | semidirect |
| 11. #447×C197 | C2 | semidirect |
| 15. #20263325 | C22 | semidirect |
| 16. #20263322 | C22 | semidirect |
| 24. D4×Dic197 | C22 | semidirect |
| 25. #20263288 | C22 | semidirect |
| 30. #20263260 | C22 | semidirect |
| 31. #20263259 | C22 | semidirect |
| 32. #20263255 | C22 | semidirect |
| 33. #20263248 | C22 | semidirect |
| 35. #20263247 | C22 | semidirect |
| 37. C8×Dic197 | C22 | semidirect |
| 96. C2×Dic197 | D8 | semidirect |
| 113. D4×C197 | #41 | semidirect |
| 149. C197 | #3100 | semidirect |
| 158. #447 | D197 | semidirect |
| 249. D4 | #15691357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161624 | 2 |
| C2×D4×Dic197 | 2 |
| #27161393 | 2 |
| #27161390 | 2 |
| #27161357 | 2 |
| #27161272 | 2 |
| #27161213 | 2 |
| D8×Dic197 | 2 |
| #27161159 | 2 |
| #27161129 | 2 |
| #447×C197 | 2 |
| #3100 | 197 |