Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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×D8×D197 | C2 | semidirect |
| 2. #27161714 | C2 | semidirect |
| 3. #27161312 | C2 | semidirect |
| 4. #27161271 | C2 | semidirect |
| 5. #27161211 | C2 | semidirect |
| 6. C4×D1576 | C2 | semidirect |
| 7. C8×D788 | C2 | semidirect |
| 8. #493×C197 | C2 | semidirect |
| 10. C2×D4×D197 | C22 | semidirect |
| 12. C2×#15691343 | C22 | semidirect |
| 14. C2×C8×D197 | C22 | semidirect |
| 16. #20263297 | C22 | semidirect |
| 19. C4×D788 | C22 | semidirect |
| 20. #20263260 | C22 | semidirect |
| 21. C4⋊#13096802 | C22 | semidirect |
| 22. #20263248 | C22 | semidirect |
| 23. #20263247 | C22 | semidirect |
| 24. #20263238 | C22 | semidirect |
| 25. C2×D8×C197 | C22 | semidirect |
| 26. C2×D8×C197 | C22 | semidirect |
| 27. #127×C197 | C22 | semidirect |
| 28. C4×C8×C197 | C22 | semidirect |
| 39. D1576 | D4 | semidirect |
| 62. D788 | D8 | semidirect |
| 63. D788 | C2×D4 | semidirect |
| 81. C8×C197 | C2×D4 | semidirect |
| 92. C2×D197 | C2×D8 | semidirect |
| 94. C4×C197 | C2×D8 | semidirect |
| 105. C197 | D4×D8 | semidirect |
| 109. #493 | D197 | semidirect |
| 120. C2×D8 | C2×D197 | semidirect |
| 121. C2×D8 | C2×D197 | semidirect |
| 123. #127 | C2×D197 | semidirect |
| 134. C4×C8 | C2×D197 | semidirect |
| 187. C8 | D4×D197 | semidirect |
| 202. C4 | D8×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D197 | 2 |
| #27161714 | 2 |
| #27161312 | 2 |
| #27161271 | 2 |
| #27161211 | 2 |
| C4×D1576 | 2 |
| C8×D788 | 2 |
| #493×C197 | 2 |
| D4×D8 | 197 |