Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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. #27161102 | C2 | semidirect |
| 5. C4×#15691337 | C2 | semidirect |
| 6. #27160838 | C2 | semidirect |
| 7. #339×C197 | C2 | semidirect |
| 10. #20263291 | C4 | semidirect |
| 11. #20263291 | C4 | semidirect |
| 12. #20263288 | C4 | semidirect |
| 13. #20263288 | C4 | semidirect |
| 71. Dic394 | C4⋊C4 | semidirect |
| 73. D788 | C4⋊C4 | semidirect |
| 124. Dic197 | #104 | semidirect |
| 131. C197 | #1806 | semidirect |
| 139. #339 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161547 | 2 |
| #27161102 | 2 |
| C2×#20263254 | 2 |
| C2×#20263252 | 2 |
| C4×#15691337 | 2 |
| #27160838 | 2 |
| #339×C197 | 2 |
| #1806 | 197 |