Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#15691345 | C2 | semidirect |
| 3. #27161653 | C2 | semidirect |
| 4. #27161553 | C2 | semidirect |
| 5. #27161297 | C2 | semidirect |
| 6. #27161283 | C2 | semidirect |
| 7. #27161107 | C2 | semidirect |
| 8. #27161073 | C2 | semidirect |
| 9. #419×C197 | C2 | semidirect |
| 18. #20263324 | C22 | semidirect |
| 19. #20263315 | C22 | semidirect |
| 26. #20263255 | C22 | semidirect |
| 27. #20263249 | C22 | semidirect |
| 28. #20263246 | C22 | semidirect |
| 32. #103×C197 | C22 | semidirect |
| 116. C197 | #3042 | semidirect |
| 125. #419 | D197 | semidirect |
| 148. #103 | 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 |
| C22×#15691345 | 2 |
| #27161653 | 2 |
| #27161553 | 2 |
| #27161297 | 2 |
| #27161283 | 2 |
| #27161107 | 2 |
| #27161073 | 2 |
| #419×C197 | 2 |
| #3042 | 197 |