Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 2. #27161441 | C2 | semidirect |
| 3. #27161436 | C2 | semidirect |
| 4. #27161087 | C2 | semidirect |
| 6. C4×#15691342 | C2 | semidirect |
| 7. #533×C197 | C2 | semidirect |
| 15. #20263249 | C22 | semidirect |
| 17. #20263237 | C22 | semidirect |
| 18. C4×#13096802 | C22 | semidirect |
| 19. C4⋊Q8×C197 | C22 | semidirect |
| 20. #125×C197 | C22 | semidirect |
| 83. C197 | #3140 | semidirect |
| 85. #533 | D197 | semidirect |
| 95. C4⋊Q8 | C2×D197 | semidirect |
| 96. #125 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263314 | 2 |
| #27161441 | 2 |
| #27161436 | 2 |
| #27161087 | 2 |
| #27161083 | 2 |
| C4×#15691342 | 2 |
| #533×C197 | 2 |
| #3140 | 197 |