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. #27161389 | C2 | semidirect |
| 4. #27161381 | C2 | semidirect |
| 5. #27161371 | C2 | semidirect |
| 6. #27161365 | C2 | semidirect |
| 7. #27161359 | C2 | semidirect |
| 8. #27161114 | C2 | semidirect |
| 9. C4⋊C8×D197 | C2 | semidirect |
| 11. #476×C197 | C2 | semidirect |
| 44. #15691357 | Q8 | semidirect |
| 134. C197 | #3076 | semidirect |
| 141. #476 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| C4×#15691357 | 2 |
| #27161389 | 2 |
| #27161381 | 2 |
| #27161371 | 2 |
| #27161365 | 2 |
| #27161359 | 2 |
| #27161114 | 2 |
| C4⋊C8×D197 | 2 |
| #27161072 | 2 |
| #476×C197 | 2 |
| #3076 | 197 |