Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 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. #27161097 | C2 | semidirect |
| 3. #27161083 | C2 | semidirect |
| 4. #27161063 | C2 | semidirect |
| 5. #410×C197 | C2 | semidirect |
| 9. C2×#15691358 | C4 | semidirect |
| 11. C22×D788 | C4 | semidirect |
| 15. C2×#15691342 | C22 | semidirect |
| 21. #117×C197 | C22 | semidirect |
| 114. C197 | #1795 | semidirect |
| 120. #410 | D197 | semidirect |
| 132. #117 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263372 | 2 |
| #27161097 | 2 |
| #27161083 | 2 |
| #27161063 | 2 |
| #410×C197 | 2 |
| #1795 | 197 |