Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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. #27161133 | C2 | semidirect |
| 3. #27160930 | C2 | semidirect |
| 4. #27160817 | C2 | semidirect |
| 5. #27160815 | C2 | semidirect |
| 9. #20263317 | C4 | semidirect |
| 10. #20263313 | C4 | semidirect |
| 13. #20263291 | C4 | semidirect |
| 15. D4×Dic197 | C4 | semidirect |
| 109. C197 | #1509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161610 | 2 |
| #27161133 | 2 |
| #27160930 | 2 |
| #27160817 | 2 |
| #27160815 | 2 |
| #27160813 | 2 |
| #327×C197 | 2 |
| #1509 | 197 |