Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#20263348 | C2 | semidirect |
| 2. C22×#15691341 | C2 | semidirect |
| 3. #27161591 | C2 | semidirect |
| 4. #27161338 | C2 | semidirect |
| 5. #27161333 | C2 | semidirect |
| 6. #27161326 | C2 | semidirect |
| 7. #27161073 | C2 | semidirect |
| 8. #427×C197 | C2 | semidirect |
| 12. C2×Dic788 | C22 | semidirect |
| 13. C2×#15691347 | C22 | semidirect |
| 14. C2×D1576 | C22 | semidirect |
| 24. #20263249 | C22 | semidirect |
| 25. #20263246 | C22 | semidirect |
| 28. #107×C197 | C22 | semidirect |
| 29. #106×C197 | C22 | semidirect |
| 54. C2×C8×C197 | D4 | semidirect |
| 105. C197 | #3054 | semidirect |
| 113. #427 | D197 | semidirect |
| 132. #107 | C2×D197 | semidirect |
| 133. #106 | C2×D197 | semidirect |
| 157. C2×C8 | D788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263348 | 2 |
| C22×#15691341 | 2 |
| #27161591 | 2 |
| #27161338 | 2 |
| #27161333 | 2 |
| #27161326 | 2 |
| #27161073 | 2 |
| #427×C197 | 2 |
| #3054 | 197 |