Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#15691342 | C2 | semidirect |
| 3. C2×#20263254 | C2 | direct (N × H) |
| 4. C22×C42×C197 | C2 | semidirect |
| 7. C2×#15691358 | C4 | semidirect |
| 9. C22×Dic394 | C4 | semidirect |
| 10. C22×D788 | C4 | semidirect |
| 14. C2×#15691342 | C22 | semidirect |
| 16. #20263254 | C22 | direct (N × H) |
| 20. C2×C42×C197 | C22 | semidirect |
| 25. #15691358 | C2×C4 | semidirect |
| 28. C2×Dic394 | C2×C4 | semidirect |
| 30. C2×D788 | C2×C4 | semidirect |
| 37. #15691342 | C23 | semidirect |
| 49. C42×C197 | C23 | semidirect |
| 53. Dic394 | C22×C4 | semidirect |
| 55. D788 | C22×C4 | semidirect |
| 79. C22×C197 | #104 | semidirect |
| 93. C2×C197 | C2×#104 | semidirect |
| 96. C197 | C22×#104 | semidirect |
| 100. C22×C42 | D197 | semidirect |
| 116. C2×C42 | C2×D197 | semidirect |
| 146. C42 | C22×D197 | semidirect |
| 178. C22 | #20263254 | direct (N × H) |
| 191. C2 | C2×#20263254 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691358 | 2 |
| C22×#15691342 | 2 |
| C2×#20263254 | 2 |
| C22×C42×C197 | 2 |
| C22×#104 | 197 |