Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#20263262 | C2 | semidirect |
| 3. #27161105 | C2 | semidirect |
| 6. #27160839 | C2 | semidirect |
| 7. #336×C197 | C2 | semidirect |
| 20. #20263251 | C4 | semidirect |
| 21. #20263251 | C4 | semidirect |
| 22. #20263248 | C4 | semidirect |
| 23. #20263248 | C4 | semidirect |
| 109. C197 | #1866 | semidirect |
| 117. #336 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263332 | 2 |
| C2×#20263262 | 2 |
| #27161105 | 2 |
| C2×#20263254 | 2 |
| #27161076 | 2 |
| #27160839 | 2 |
| #336×C197 | 2 |
| #1866 | 197 |