Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#20263354 | C2 | semidirect |
| 2. #27161725 | C2 | semidirect |
| 3. #27161463 | C2 | semidirect |
| 4. #27161325 | C2 | semidirect |
| 5. #27161295 | C2 | semidirect |
| 6. #27161243 | C2 | semidirect |
| 7. #27161215 | C2 | semidirect |
| 8. C4×D1576 | C2 | semidirect |
| 9. #436×C197 | C2 | semidirect |
| 11. C22×D788 | C22 | semidirect |
| 13. C2×Dic788 | C22 | semidirect |
| 14. C2×#15691347 | C22 | semidirect |
| 15. C2×#15691347 | C22 | semidirect |
| 19. #20263314 | C22 | semidirect |
| 21. #20263305 | C22 | semidirect |
| 25. C4×D788 | C22 | semidirect |
| 27. #20263260 | C22 | semidirect |
| 28. #20263251 | C22 | semidirect |
| 29. #20263248 | C22 | semidirect |
| 30. #20263248 | C22 | semidirect |
| 31. C2×M16×C197 | C22 | semidirect |
| 33. C4⋊C8×C197 | C22 | semidirect |
| 34. C22⋊C8×C197 | C22 | semidirect |
| 35. C4×C8×C197 | C22 | semidirect |
| 54. D1576 | D4 | semidirect |
| 124. C197 | #3273 | semidirect |
| 134. #436 | D197 | semidirect |
| 144. C2×M16 | C2×D197 | semidirect |
| 155. C4⋊C8 | C2×D197 | semidirect |
| 159. C22⋊C8 | C2×D197 | semidirect |
| 160. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263354 | 2 |
| #27161725 | 2 |
| #27161463 | 2 |
| #27161325 | 2 |
| #27161295 | 2 |
| #27161243 | 2 |
| #27161215 | 2 |
| C4×D1576 | 2 |
| #436×C197 | 2 |
| #3273 | 197 |