Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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. #27161095 | C2 | semidirect |
| 3. #27161089 | C2 | semidirect |
| 4. #27161053 | C2 | semidirect |
| 5. #413×C197 | C2 | semidirect |
| 8. C2×#15691358 | C4 | semidirect |
| 12. C22×Dic394 | C4 | semidirect |
| 108. C197 | #1796 | semidirect |
| 113. #413 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263373 | 2 |
| #27161095 | 2 |
| #27161089 | 2 |
| #27161053 | 2 |
| #413×C197 | 2 |
| #1796 | 197 |