Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 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. #27161435 | C2 | semidirect |
| 4. #27161432 | C2 | semidirect |
| 5. #27161428 | C2 | semidirect |
| 6. #27161424 | C2 | semidirect |
| 7. #27161076 | C2 | semidirect |
| 8. #27161075 | C2 | semidirect |
| 9. #27161073 | C2 | semidirect |
| 10. C2×C8×Dic197 | C2 | semidirect |
| 11. #416×C197 | C2 | semidirect |
| 125. C197 | #3131 | semidirect |
| 136. #416 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161632 | 2 |
| #27161625 | 2 |
| #27161435 | 2 |
| #27161432 | 2 |
| #27161428 | 2 |
| #27161424 | 2 |
| #27161076 | 2 |
| #27161075 | 2 |
| #27161073 | 2 |
| C2×C8×Dic197 | 2 |
| #416×C197 | 2 |
| #3131 | 197 |