Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
704 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 161 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×#20263356 | C2 | semidirect |
| 2. #27161650 | C2 | semidirect |
| 3. #27161262 | C2 | semidirect |
| 4. #27161257 | C2 | semidirect |
| 5. #27161096 | C2 | semidirect |
| 6. #27161063 | C2 | semidirect |
| 8. C22×Dic394 | C22 | semidirect |
| 10. #20263356 | C22 | semidirect |
| 13. C2×#15691342 | C22 | semidirect |
| 14. #20263324 | C22 | semidirect |
| 15. #20263313 | C22 | semidirect |
| 18. #20263285 | C22 | semidirect |
| 19. #20263253 | C22 | semidirect |
| 20. #20263245 | C22 | semidirect |
| 21. #20263243 | C22 | semidirect |
| 129. C197 | #3022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263356 | 2 |
| #27161650 | 2 |
| #27161262 | 2 |
| #27161257 | 2 |
| #27161096 | 2 |
| #27161063 | 2 |
| #585×C197 | 2 |
| #3022 | 197 |