Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#20263352 | C2 | semidirect |
| 2. #27161629 | C2 | semidirect |
| 3. #27161466 | C2 | semidirect |
| 4. #27161455 | C2 | semidirect |
| 5. #27161451 | C2 | semidirect |
| 6. C4×#15691342 | C2 | semidirect |
| 7. C2×#127×C197 | C2 | semidirect |
| 10. C2×#15691346 | C22 | semidirect |
| 11. C2×#15691343 | C22 | semidirect |
| 13. #20263326 | C22 | semidirect |
| 14. #20263323 | C22 | semidirect |
| 15. #20263314 | C22 | semidirect |
| 18. #20263237 | C22 | semidirect |
| 19. C4×#13096802 | C22 | semidirect |
| 34. #15691342 | D4 | semidirect |
| 57. #13096802 | C2×D4 | semidirect |
| 82. C4×C197 | AGL(1,ℤ/8) | semidirect |
| 90. C197 | #3151 | semidirect |
| 94. C2×#127 | D197 | semidirect |
| 174. C4 | #20263352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263352 | 2 |
| #27161629 | 2 |
| #27161466 | 2 |
| #27161455 | 2 |
| #27161451 | 2 |
| C4×#15691342 | 2 |
| C2×#127×C197 | 2 |
| #3151 | 197 |