Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C2×#20263284 | C2 | semidirect |
| 3. #27161419 | C2 | semidirect |
| 4. #27161418 | C2 | semidirect |
| 5. #27161402 | C2 | semidirect |
| 6. #27161401 | C2 | semidirect |
| 7. #27161121 | C2 | semidirect |
| 8. #27161119 | C2 | semidirect |
| 9. #27161080 | C2 | semidirect |
| 10. #27161042 | C2 | semidirect |
| 11. #417×C197 | C2 | semidirect |
| 30. #20263260 | C22 | semidirect |
| 31. #20263259 | C22 | semidirect |
| 32. #20263258 | C22 | semidirect |
| 33. #20263257 | C22 | semidirect |
| 34. #20263250 | C22 | semidirect |
| 35. #20263247 | C22 | semidirect |
| 41. #103×C197 | C22 | semidirect |
| 42. #102×C197 | C22 | semidirect |
| 152. C197 | #3093 | semidirect |
| 163. #417 | D197 | semidirect |
| 191. #103 | C2×D197 | semidirect |
| 193. #102 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161586 | 2 |
| C2×#20263284 | 2 |
| #27161419 | 2 |
| #27161418 | 2 |
| #27161402 | 2 |
| #27161401 | 2 |
| #27161121 | 2 |
| #27161119 | 2 |
| #27161080 | 2 |
| #27161042 | 2 |
| #417×C197 | 2 |
| #3093 | 197 |