Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161750 | C2 | semidirect |
| 2. #27161744 | C2 | semidirect |
| 3. #27161427 | C2 | semidirect |
| 4. #27161424 | C2 | semidirect |
| 5. #27161358 | C2 | semidirect |
| 6. #27161275 | C2 | semidirect |
| 7. #27161273 | C2 | semidirect |
| 8. #27161203 | C2 | semidirect |
| 9. #27161161 | C2 | semidirect |
| 10. C4×#15691343 | C2 | semidirect |
| 11. #474×C197 | C2 | semidirect |
| 78. Dic394 | D8 | semidirect |
| 84. D788 | #41 | semidirect |
| 131. C197 | #3358 | semidirect |
| 138. #474 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161750 | 2 |
| #27161744 | 2 |
| #27161427 | 2 |
| #27161424 | 2 |
| #27161358 | 2 |
| #27161275 | 2 |
| #27161273 | 2 |
| #27161203 | 2 |
| #27161161 | 2 |
| C4×#15691343 | 2 |
| #474×C197 | 2 |
| #3358 | 197 |