Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 1. #27161632 | C2 | semidirect |
| 3. #27161440 | C2 | semidirect |
| 4. #27161435 | C2 | semidirect |
| 5. #27161088 | C2 | semidirect |
| 8. M16×Dic197 | C2 | semidirect |
| 9. #419×C197 | C2 | semidirect |
| 12. #20263325 | C22 | semidirect |
| 13. #20263317 | C22 | semidirect |
| 22. #20263250 | C22 | semidirect |
| 25. #20263236 | C22 | semidirect |
| 26. C8×Dic197 | C22 | semidirect |
| 30. #103×C197 | C22 | semidirect |
| 104. C197 | #3140 | semidirect |
| 111. #419 | D197 | semidirect |
| 131. #103 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161632 | 2 |
| C2×#20263315 | 2 |
| #27161440 | 2 |
| #27161435 | 2 |
| #27161088 | 2 |
| #27161085 | 2 |
| #27161083 | 2 |
| M16×Dic197 | 2 |
| #419×C197 | 2 |
| #3140 | 197 |