Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #27161383 | C2 | semidirect |
| 4. #27161286 | C2 | semidirect |
| 6. #27161184 | C2 | semidirect |
| 7. C4×#15691348 | C2 | semidirect |
| 95. C197 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161556 | 2 |
| #27161417 | 2 |
| #27161383 | 2 |
| #27161286 | 2 |
| #27161234 | 2 |
| #27161184 | 2 |
| C4×#15691348 | 2 |
| #27161140 | 2 |
| #541×C197 | 2 |
| #3127 | 197 |