Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161417 | C2 | semidirect |
| 3. #27161371 | C2 | semidirect |
| 4. #27161366 | C2 | semidirect |
| 5. #27161286 | C2 | semidirect |
| 6. #27161281 | C2 | semidirect |
| 8. #27161184 | C2 | semidirect |
| 9. #27161177 | C2 | semidirect |
| 10. #27161136 | C2 | semidirect |
| 11. #533×C197 | C2 | semidirect |
| 136. C197 | #3116 | semidirect |
| 138. #533 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15691358 | 2 |
| #27161417 | 2 |
| #27161371 | 2 |
| #27161366 | 2 |
| #27161286 | 2 |
| #27161281 | 2 |
| #27161239 | 2 |
| #27161184 | 2 |
| #27161177 | 2 |
| #27161136 | 2 |
| #533×C197 | 2 |
| #3116 | 197 |