Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#20263350 | C2 | semidirect |
| 2. #27161627 | C2 | semidirect |
| 3. #127×D197 | C2 | semidirect |
| 4. #27161467 | C2 | semidirect |
| 5. #27161455 | C2 | semidirect |
| 6. #27161452 | C2 | semidirect |
| 7. #27161451 | C2 | semidirect |
| 8. C4×#15691341 | C2 | semidirect |
| 9. #493×C197 | C2 | semidirect |
| 14. C2×#15691347 | C22 | semidirect |
| 15. C2×#15691346 | C22 | semidirect |
| 16. C2×#15691343 | C22 | semidirect |
| 18. #20263326 | C22 | semidirect |
| 22. #20263313 | C22 | semidirect |
| 26. #20263236 | C22 | semidirect |
| 27. C4×#13096802 | C22 | semidirect |
| 28. C2×D8×C197 | C22 | semidirect |
| 30. #127×C197 | C22 | semidirect |
| 31. C4×C8×C197 | C22 | semidirect |
| 48. #15691341 | D4 | semidirect |
| 77. #13096802 | C2×D4 | semidirect |
| 86. C8×C197 | C2×D4 | semidirect |
| 97. C4×C197 | AGL(1,ℤ/8) | semidirect |
| 108. C197 | #3151 | semidirect |
| 115. #493 | D197 | semidirect |
| 126. C2×D8 | C2×D197 | semidirect |
| 133. #127 | C2×D197 | semidirect |
| 140. C4×C8 | C2×D197 | semidirect |
| 195. C8 | D4×D197 | semidirect |
| 209. C4 | #20263350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263350 | 2 |
| #27161627 | 2 |
| #127×D197 | 2 |
| #27161467 | 2 |
| #27161455 | 2 |
| #27161452 | 2 |
| #27161451 | 2 |
| C4×#15691341 | 2 |
| #493×C197 | 2 |
| #3151 | 197 |