Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 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. #27161632 | C2 | semidirect |
| 3. #27161442 | C2 | semidirect |
| 4. #27161424 | C2 | semidirect |
| 5. #27161085 | C2 | semidirect |
| 6. #27161084 | C2 | semidirect |
| 7. #27161083 | C2 | semidirect |
| 8. M16×Dic197 | C2 | semidirect |
| 9. #418×C197 | C2 | semidirect |
| 13. #20263325 | C22 | semidirect |
| 17. #20263317 | C22 | semidirect |
| 22. #20263248 | C22 | semidirect |
| 23. #20263247 | C22 | semidirect |
| 24. #20263246 | C22 | semidirect |
| 25. #20263236 | C22 | semidirect |
| 26. C8×Dic197 | C22 | semidirect |
| 30. #102×C197 | C22 | semidirect |
| 111. C197 | #3138 | semidirect |
| 120. #418 | D197 | semidirect |
| 140. #102 | 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×#20263322 | 2 |
| #27161442 | 2 |
| #27161424 | 2 |
| #27161085 | 2 |
| #27161084 | 2 |
| #27161083 | 2 |
| M16×Dic197 | 2 |
| #418×C197 | 2 |
| #3138 | 197 |