Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #27161035 | C2 | semidirect |
| 5. C2×#20263237 | C2 | semidirect |
| 6. #27160843 | C2 | semidirect |
| 7. #339×C197 | C2 | semidirect |
| 10. #20263334 | C4 | semidirect |
| 16. #20263254 | C4 | semidirect |
| 17. #20263249 | C4 | semidirect |
| 18. #20263246 | C4 | semidirect |
| 98. C197 | #1765 | semidirect |
| 106. #339 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263334 | 2 |
| C2×#20263254 | 2 |
| #27161073 | 2 |
| #27161035 | 2 |
| C2×#20263237 | 2 |
| #27160843 | 2 |
| #339×C197 | 2 |
| #1765 | 197 |