Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27161366 | C2 | semidirect |
| 3. #27160823 | C2 | semidirect |
| 4. #27160808 | C2 | semidirect |
| 5. #492×C197 | C2 | semidirect |
| 11. C4⋊#13096802 | C22 | semidirect |
| 14. C4⋊Q8×C197 | C22 | semidirect |
| 16. C4×C8×C197 | C22 | semidirect |
| 38. D788 | SD16 | semidirect |
| 69. C197 | #1629 | semidirect |
| 72. #492 | D197 | semidirect |
| 78. C4⋊Q8 | C2×D197 | semidirect |
| 86. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161714 | 2 |
| #27161366 | 2 |
| #27160823 | 2 |
| #27160808 | 2 |
| #492×C197 | 2 |
| #1629 | 197 |