Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#20263359 | C2 | semidirect |
| 3. C2×#20263314 | C2 | semidirect |
| 4. C4×#15691358 | C2 | semidirect |
| 5. #27161302 | C2 | semidirect |
| 6. #27161295 | C2 | semidirect |
| 7. #27161089 | C2 | semidirect |
| 8. #27161085 | C2 | semidirect |
| 9. #423×C197 | C2 | semidirect |
| 15. C2×Dic788 | C22 | semidirect |
| 17. C2×#15691347 | C22 | semidirect |
| 22. C4×Dic394 | C22 | semidirect |
| 23. C4×D788 | C22 | semidirect |
| 29. #20263251 | C22 | semidirect |
| 34. C4⋊C8×C197 | C22 | semidirect |
| 125. C197 | #3040 | semidirect |
| 133. #423 | D197 | semidirect |
| 158. C4⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263359 | 2 |
| C2×#20263354 | 2 |
| C2×#20263314 | 2 |
| C4×#15691358 | 2 |
| #27161302 | 2 |
| #27161295 | 2 |
| #27161089 | 2 |
| #27161085 | 2 |
| #423×C197 | 2 |
| #3040 | 197 |