Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#20263353 | C2 | semidirect |
| 2. #27161722 | C2 | semidirect |
| 3. #27161322 | C2 | semidirect |
| 4. #27161291 | C2 | semidirect |
| 5. #27161240 | C2 | semidirect |
| 6. #27161211 | C2 | semidirect |
| 7. C4×D1576 | C2 | semidirect |
| 8. #27161158 | C2 | semidirect |
| 9. #495×C197 | C2 | semidirect |
| 11. C2×D4×D197 | C22 | semidirect |
| 13. C2×#15691345 | C22 | semidirect |
| 16. C2×#15691341 | C22 | semidirect |
| 18. #20263302 | C22 | semidirect |
| 23. C4×D788 | C22 | semidirect |
| 25. #20263260 | C22 | semidirect |
| 26. C4⋊#13096802 | C22 | semidirect |
| 27. #20263250 | C22 | semidirect |
| 28. #20263248 | C22 | semidirect |
| 29. #20263247 | C22 | semidirect |
| 30. #20263238 | C22 | semidirect |
| 31. C2×Q16×C197 | C22 | semidirect |
| 32. C2×SD16×C197 | C22 | semidirect |
| 34. #124×C197 | C22 | semidirect |
| 35. C4×C8×C197 | C22 | semidirect |
| 50. D1576 | D4 | semidirect |
| 124. C197 | #3273 | semidirect |
| 128. #495 | D197 | semidirect |
| 138. C2×Q16 | C2×D197 | semidirect |
| 140. C2×SD16 | C2×D197 | semidirect |
| 145. #124 | 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×#20263353 | 2 |
| #27161722 | 2 |
| #27161322 | 2 |
| #27161291 | 2 |
| #27161240 | 2 |
| #27161211 | 2 |
| C4×D1576 | 2 |
| #27161158 | 2 |
| #495×C197 | 2 |
| #3273 | 197 |