Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 5. #27161362 | C2 | semidirect |
| 6. #27161287 | C2 | semidirect |
| 8. #27161186 | C2 | semidirect |
| 9. #27161183 | C2 | semidirect |
| 127. C197 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161631 | 2 |
| C2×Q8×Dic197 | 2 |
| #27161410 | 2 |
| #27161407 | 2 |
| #27161362 | 2 |
| #27161287 | 2 |
| #27161235 | 2 |
| #27161186 | 2 |
| #27161183 | 2 |
| #27161133 | 2 |
| #451×C197 | 2 |
| #3113 | 197 |