Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27161557 | C2 | semidirect |
| 4. #27161303 | C2 | semidirect |
| 5. #27161287 | C2 | semidirect |
| 6. #27161105 | C2 | semidirect |
| 7. #27161088 | C2 | semidirect |
| 9. C22×Q16×C197 | C2 | semidirect |
| 111. C197 | #3044 | semidirect |
| 114. C22×Q16 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263357 | 2 |
| #27161653 | 2 |
| #27161557 | 2 |
| #27161303 | 2 |
| #27161287 | 2 |
| #27161105 | 2 |
| #27161088 | 2 |
| #27161076 | 2 |
| C22×Q16×C197 | 2 |
| #3044 | 197 |