Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #27161634 | C2 | semidirect |
| 3. #27161388 | C2 | semidirect |
| 4. #27161382 | C2 | semidirect |
| 5. #27161366 | C2 | semidirect |
| 6. #27161364 | C2 | semidirect |
| 7. #27161360 | C2 | semidirect |
| 8. #27161116 | C2 | semidirect |
| 9. C4⋊C8×D197 | C2 | semidirect |
| 11. #477×C197 | C2 | semidirect |
| 44. #15691359 | Q8 | semidirect |
| 134. C197 | #3076 | semidirect |
| 140. #477 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| C4×#15691359 | 2 |
| #27161388 | 2 |
| #27161382 | 2 |
| #27161366 | 2 |
| #27161364 | 2 |
| #27161360 | 2 |
| #27161116 | 2 |
| C4⋊C8×D197 | 2 |
| #27161074 | 2 |
| #477×C197 | 2 |
| #3076 | 197 |