Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 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. #27161197 | C2 | semidirect |
| 3. #27160909 | C2 | semidirect |
| 4. #27160887 | C2 | semidirect |
| 5. C4×C16×C197 | C2 | semidirect |
| 8. Dic1576 | C4 | semidirect |
| 9. #20263271 | C4 | semidirect |
| 10. D3152 | C4 | semidirect |
| 49. C197 | #2178 | semidirect |
| 55. C4×C16 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161511 | 2 |
| #27161197 | 2 |
| #27160909 | 2 |
| #27160887 | 2 |
| C4×C16×C197 | 2 |
| #2178 | 197 |